I have a horse with heaves and it is VERY manageable, if you can figure out what works. My BO also has an older horse with heaves, who was out on a long term lease, and his did progress over the years, but his condition was vastly different from my own horse (indoor arena, standard feed, constant work whilst in heaving state ... he found out about this after). Just to give perspective, my horse was competing at 2nd level dressage and working 4-5 days per week without issue, but we caught things early and promptly executed an action plan.
So I think much would depend on what stage this horse is at. My own horse was absolutely terrible when he first started showing heaves: wheezing, excessive coughing, even at the walk. I though for sure he would never improve. But, I ended up moving him to a well ventilated barn with great hay (square bales), changed his feed, monitored his condition and made sure I had the proper medication on hand. Your main concern is reducing frequency of flare ups.
First thing is that hay needs to be good! Dusty hay will make things worse and if your horse is on a roundbale all day, he will breathe in the spores and that will flare him up! My horse has been on great quality square bales for several years now, not soaked and 24/7 turnout.
Nutrition is also important. My horse was previous on feed that was higher in sugars and omega 6,which over all just wasn't good for him. I did some reading and switched him to a vitamin/mineral supplement which I fed with some soaked hay cubes and added some flax (at the time). Omega 6 is necessary, but it is more pro-inflammatory than neutral in the absence of Omega-3. Upping the Omega 3 and lowering the Omega 6 was better for a inflammatory condition such as heaves. I also added MSM for the same reason.
Because I'm a nerd and wanted to log conditions to see when my horse was more at risk for flaring up, I took his respiration rate at relatively the same time of day, regularly for at least a year and then at least a few times a month for the 2nd and third year. This would be specific for your horse, but the patterns I found were that he would flare up when: the weather started getting colder, after vaccinations, dry/hot summer days, when he became unfit and if we had a less stellar bale of hay. In general, the number of flare ups went down over the 3 years and his respiration average went from around the mid 20s the first year, to about 18, and last I checked it was around 16 (in the norm), so it did go down as we figured out how to avoid flare ups. He was also seemingly better off when kept in work, which the vet had also suggested as therapeutic conditioning for the lungs and I'd imagine preventing extra weight on the lungs too. The 4th year, we briefly moved to another barn with different practices/ conditions and his respiration went back up a bit and coughing started up some in the morning. That place used sand in the stalls and fed a different feed (purina) that we tried, but it just didn't work for us. After moving back, we have had no issues since.
Now, you absolutely should have the adequate medication at hand for bad flare ups. Just as with an allergy attack (essentially what it is), you want to slow down the inflammation to prevent/reduce any damage from occurring. This is essential and always have that medication handy, when needed. But I think one mistake people make is using medication TOO much. Glucocorticoid medication, such as "Dex" is a synthetic corticosteroid to mimic what your horse's cortisol already does. Basically, it goes in to enhance the levels of defense against the inflammation when the inflammation is just too much for the body to handle. However, when it becomes a frequent 'crutch', your horse becomes at risk for what is called suppression of the hypothalamic–pituitary–adrenal (HPA) axis or in other words, adrenal insufficiency. Essentially, the horse's adrenal gland, which produces the cortisol (anti-inflammatory efforts), can no longer hold a candle to the synthetic levels and 'burns out'. This is also why steroids need to be tapered, by the way. The body now becomes reliant on the medication to fight the inflammation, even at lower levels. I don't mention this to say medication is bad, because it is actually a godsend for managing the condition. But instead, I mention it because I think many are now aware that "steroids are hard on the body", but not necessarily how nor that there is potential of them being counter productive to the very condition they are trying to manage.
So when should it be used? I used it most frequently at the beginning stages, when flare ups were at their strongest. If I saw heave lines, excessive movement of the accessory muscles, heard choking type sounds or if I otherwise had the bad feeling. These are all times I would use medication then and there. Otherwise, my vet had suggested some alternative methods to help move mucous and calm the allergies by trying to trot the horse (on lunge) very briefly to try and move some of the mucous and also take away any potential allergens, meaning out doors for us and no brushing that would lift up dust. If it were warm, I'd even hose off my horse to lock down any dust, and I also used oral cough syrups such as Respi-free by Omega Alpha or Zev. The main thing is to your best to stop the allergies from getting triggered and use your own judgement. If your unsure, use the medication.
As for how things turned out, It has been 2 years since my horse has had any flare up at all (6 years since he was diagnosed). He occasionally coughs in the mornings, but then he is good for the day. He is retired now (due to another reason), but I am happy his breathing is well off. My Bo's horse, who is much more advanced in heaves, has her struggles and she has gotten better since she has been back with the BO and stuff is being managed better for her condition, but I unfortunately think because she has had years and years of little to no management, that the damage is done and her condition isn't going to get much better like my horse's did. That being said, the vet still recommends my BO that some exercise is the best therapy for the lungs.
SO, to directly answer your question, I think the horse you are looking at could be a good fit and a light trail ride here and there should not be a problem unless the horse is (1) critically advanced and (2) vastly triggered by the spring/summer spores etc. But, you need to take into account whether you can adequately manage the environmental conditions for this horse and if that is something you want to take on in comparison to a horse with no issues.