The 1860 Henry rifle clones made by Uberti and sold by various firms are indeed weaker than modern lever action designs by Marlin, Winchester and others, because of the toggle link locking system and brass frame, but they are safe with standard pressure ammo. Do not use +P ammunition in these rifles.
The Hornady Leverevolution .45 Colt load is a standard pressure load and would be safe in the Henry. It would do a good job on hogs or deer, assuming you put the bullet where it is supposed to go. Actually, the same could be said of most any standard pressure .45 Colt load from a rifle. You will get a half-inch hole through the deer and it will probably run 50 yards and fall down dead.
From a functioning standpoint, the toggle link rifles can be sensitive to cartridge overall length, so the ammunition should be fairly close to standard length. If the rounds are too long or too short, the catridge elevator can bind. There is some room for variance in the design, but it can be a concern with ammo that is unusually short or long.
The sights on the 1860 are fairly crude, but duplicate the originals quite well. I would expect that you would be getting goups at 100 yards that would be usable on a deer (about 4 to 6 inches or so), but do not expect anything close to MOA. The good news is that by the time your accuracy starts to limit you, the ballistics of the cartridge have pretty much pooped out too.
The 1860's are very cool and fun to shoot. I had one in .44/40 for quite a few years and it was a great rifle for fun on the range.