Freeze peanut butter and treats/food in the kong. (Make sure the peanut butter doesn't have artificial sweetener in it, because that's a thing and it can kill your dog.) Puzzle toys, treat dispensing toys, or hide the treat are fun for the dog too (I take a few small training treats and hide them around the house while the dog is locked in the laundry room, then I let her out to go find them.) Of course you have to be careful with these because you're feeding the dog which does offset some of the benefits of the activity. I don't know how much space you can make inside but something like this could help: https://www.amazon.com/gp/aw/d/B00MRBF4ME/ref=pd_aw_sbs_199_3?ie=UTF8&psc=1&refRID=AX03X7ET648CYVF8CQ9Y&dpPl=1&dpID=71IF0DMiMiL Or if you have a treadmill, I have walked our dog on mine in the winter when the weather was bad. My tips for that are to have the dog stand on the belt and start it from there at the slowest speed possible, then work your way up. And to do short walks on the treadmill until the dog gets used to it. I don't know how different a dog's paw pads are to a person's foot soles, but I have walked barefoot on a treadmill before and it was kinda uncomfortable, and I am the kind of person who wears shoes as little as possible. Good luck and what a cute pooch!
Thank you, Dala! The Kong is a godsend, and I love the idea of hiding the treats around the house! He really likes digging, so I'm thinking of building a little sandpit for him in the yard and hiding treats and chewtoys in it. Luckily, my landlords are incredible, and they've been helping me re-fit our yard to be more dog friendly for him. Pretty soon, I'm going to feel comfortable leaving him in the yard when I'm home.
Our mutty girl is also a rescue who was an adult dog when we got her. Our experience has been that she has mellowed out quite a bit since we have had her - it may take awhile for him to realize that you are his people and hopefully when he does he will chill out a bit. Our dog was fairly anxious at the beginning, especially the first few weeks/months. Take things slow with your new guy and he should relax some as he begins to trust you more.