Classic gun, but it had a couple problems corrected in the later Winchester. For one you have to remove the magazine to reload it, whereas on a Winchester you load through the side port and can top off as you shoot. Also if you shoot a lot of rounds the barrel gets hot, and there’s no fore stock to keep your hand from being burned.
"Remove the magazine"? All you do is slide the magazine follower forward towards the muzzle and the twist the muzzle cap to the side and pour rounds down the tube, base first. Not totally convenient to do from the prone but fast and easy with practice. Actually faster than the side gate loading, which is one at a time.
As far as barrel heating goes, you'd have to be in an all day firefight to get a Henry to heat up enough to burn your hand. It's a small cartridge and that barrel is a giant heat sink: no way will it get hot after a single magazine load. Or even two or three.
The real problem with the lack of a handguard was that the magazine follower could stop on your hand if you weren't paying attention and cause a failure to feed. That, and the magazine had that slot in the bottom which left the magazine vulnerable to dirt and impact damage.