If I have an AR pistol in 350 Legend, I can use it in shotgun and late muzzleloader season for deer, right?

Yes. But be prepared for a DNR officer to argue with you.

I got my license checked during bow season, had my .357 on my belt. Officer absolutely insisted I couldn't carry while bowhunting. Said he wasn't going to ticket me but you can't carry a handgun at all while bowhunting.

I had to get adamant with him before he'd even look up whether or not I was right. Depending on county you're bound to run into a similar officer if you're using something nontraditional like that. Keep the regs in your pocket and show him "This says it's OK."

You would think they would know the law