They are just as accurate as any other out of the box .22. Really cool and inexpensive gun. Like I said, downfall is you're stuck to Henry 8rd mags.

The Henry I had would function just fine if you just loaded one less round in the mags. The front sight left a good bit to be desired though. In fact I replaced that craptastic plastic FS with a metal ramp. Lots of flex in that plastic with a steel liner barrel too.

I always wondered if you use a metal (I think it was aluminum with a steel liner) Charter Arms barrel on the Henry?

AR7.com offers steel barrels for the AR-7, you can get sporter weight or even bull target barrels. I have not heard very good things about the plastic or aluminum sleaved barrels for the AR-7.

I own a few Ruger 10-22TD's and Marlin Papoose's as well as the Rossi matched pair/Trifecta. As much fun as they are, and as handy as they are to throw in the car or truck or ATV for a trip, I would still opt for a non takedown for a heavy duty end of times survival type rifle.
That being said, I would take a mostly stock stainless synthetic 10-22 with see-thru style scope mounts. Get a good sling an extra mag and some ammo, maybe fill the inside of the stock with a knife and lighter, cleaning kit etc. A lot of people complain about detachable magazine fed rifle for survival, "what if you lose your mag?"  If something did happen to the mag, you can always single load it, hunting small game it is not a big deal.

I did at one point lust after the Marlin 81T, a tube fed stainless synthetic or laminate bolt action .22 that can take almost any kind of .22 ammo. Marlin discontinued the 81T, and when its replacement showed up the XT-22TSR, I bought the first one I found for sale. It ended up being a steaming pile of crap, the worst new rifle I have ever purchased, It took a couple trips back to Remington before being replaced with a used/returned rifle that had a lot of scratches and dings in it.

And as far as hunting game with a handgun, I got my first .22pistol at 14yo and put 500rds through it almost every week for a couple of years. I then started buying more pistols in .22lr and bigger and have enjoyed hunting with handguns ever since. I have shot a Jackrabbit at a ranged 220yds with a .17hmr pistol with 2x scope, my Ruger Charger can hit clays consistantly at 100yds with a 2-7x scope and bipod. I have killed many squirrels and rabbits out to 60yds with iron sights on a Ruger MKII, S&W 2206, Beretta Neos, etc. I practice at 100yds a lot with the little 1lb propane cylinders with .22's, 9mm's and .357's. It is more challenging than a rifle, no debate there, but if there is abundant game I would feel plenty comfortable with a handgun. The Native Americans survived with bows and spears, I know that not every hunt was succesfull and that they had a tribe of hunters, but I think that a pistol has the same range as a primitive arrow or better.