Dewormers are not all the same. Whether it is safe or not would depend largely on what particular dewormer is and how much you are giving.
"Dewormer" is a very large category. Before I went saying "oh its fine" potentially risking my horse harm- I would find out WHICH dewormer it is, what the main active ingredient is as the dewormer, and go from there.
Moxidectin has been the subject of controversy and for good reason. It is the only horse wormer that is capable of killing the above larvae in a single dose, which is a very impressive feat. CAUTION: Its liability is that the overdose tolerance threshold is far less than other wormers; 5 times the standard dose can cause significant damage to your horse. Whereas it may be difficult to give an adult horse an overdose 5 times the standard dose, it's extremely easy to make this mistake when worming a foal. As such, at no time would I recommend using this wormer on foals or weakened horses.
The most popular Moxidectin-based wormer is Quest.
Only a few different wormers are dangerous to overdose with. Most others have either a x10 health warning rate, meaning that you'd have to severely overdose for anything to happen. I'd read the warning labels on the tube and look the brand up if I were you. We use Safeguard and it actually has a reading on the tube that says what a safe amount to use is, when you should contact a vet, and symptoms of overdose on it.
I'd really only be worried if you have a wormer with Moxidectin or a Mixidectin derivitive/compound in it, but its good to check just in case.
I used strongoid paste (pyrantel) this time. I usually hand my wormer to someone standing next to me to administer :) but wanted to do it myself this time. I wasn't so confident in my aiming/handling abilities, and I wanted to make sure if I got too much in there it wasnt the worst thing in the world. Apparently gorilla didnt care one bit, and didnt move when I stuck it in the corner of his mouth and shot it in. I got 900lbs in. Thank you guys for the replies, i'm glad im more informed now!
I've heard zimectrin gold is one to be careful with too (not that one shouldn't be careful with all of them...), so is the 'ivermectin' category generally more dangerous than the others? Quest is ivermectin, right?