Yep, you certainly don't want more fat on your mare; any more and you'd be pushing her into unhealthy. While fat would "smooth out" her conformation - and this is often done to help camouflage certain aspects of conformation not considered show ideal, in show horses, such as the longish back in your mare, which by the way isn't a problem for riding her - to increase her fat levels to "show condition" would make her more prone to health problems such as laminitis, metabolic syndrome etc.
Of course, your mare's shape will become more athletic still with work - and I second
's call for preferencing actual trail riding through terrain like hilly country or sandy country if you have those, to working the poor things around and around in circles. I think some round pen work is OK but my upper limit was always 15-20 minutes in a session (walk-trot-canter), every alternate day, and more trail or general riding than anything, and not in the arena on a day where they'd already had round pen work / lunging. We didn't build a round pen when we bought our rural property in 2010 because I don't actually find them crucial for saddle training or general training of horses. The best thing about them is being able to do liberty lunging, which is more fun than line lunging.
You're unlikely to find any "nasty" in your mare as most STBs are kind, cooperative horses with a brilliant work ethic, so just enjoy.
They are very straightforward, and intelligent, and (unless they've had bad experiences) they like hanging out with people, and going on adventures with you. Also they're generally very calm horses (especially off-track STBs compared to off-track thoroughbreds). There's cart horse genes in them going way back, and also their racing is a bit less crazy-making than TB racing as they mostly do running starts from behind mobile barriers, rather than standing starts, and are never cooped up in boxes that release them at the start - that kind of standstill-to-flat-out, from being in a cage, is quite crazy-making for many horses.
I'm assuming your mare was trained for racing? Maybe raced? Harness racing horses that have trained on track are very used to cars and trucks as they are familiar with mobile barriers on track, and lining up behind those, and also with watering trucks making their way around the racetrack when horses are doing preliminaries for trials etc. So this tends to make them less spooky around traffic, as long as they can see it coming and it doesn't get in their personal space.
About voice cues, there isn't a magic word or anything, it depends on how each trainer cues. You don't have to find the same word as her last trainer, you can get her used to your own cues as she gets to know you. Most harness trainers will use "whoa" to help cue the horse to slow down, and tongue-click to get them walking on, going faster etc. Just cue her consistently - when you're leading on the halter, "whoa" if that's what you want to use, starting just before providing resistance on the halter and stopping yourself. Praise when she does it, repeat until she's got your cue. Same with tongue-clicking, walk-on or whatever you're going to use, to start walking from a standstill.
Is this mare saddle trained already, or are you going to do that?
These horses are usually a pleasure to be around and work with, so congratulations on your acquisition - I'm sure Rose will love being a trail horse.
And this is the horse I ride, whom I saddle trained back in 2009 after he came off-track. He's wonderful.
PS on stopping: This can cause some issues because of confusion when you're first riding an OTSTB, because in their harness careers they were mostly only asked to stop after completing certain predictable intervals, say 400m or 800m sprints, or race distance. ("What do you mean, stop? I must be misunderstanding you. I've not even done any work yet!") And then, the stop cue is often to loosen the reins, which is the opposite of what horse riders do - just as taking up the reins means, "We're going to run now!" on the harness track. So you have to re-cue them for saddle training - many a hapless soul has ended up going at race pace on a keen STB when pulling on the reins in an effort to slow them down. This can be vastly amusing to harness racing insider onlookers, but not so much to a rider not used to going fast and not knowing when the horse is going to stop (if that happens, it's usually quite amenable to slowing down after 2100m, which is standard race distance in Australia). And then you go back to working on communication. (Or you prevent that situation because you know it could happen!