I agree that you should still take him for long walks. If you can't get him out for a good walk than you could use a treadmill, but I wouldn't use it everyday. Also if you're going to use a treadmill please seek out a safe way to do so, doing it wrong could be very dangerous. Try to get him out for walks as much as possible, there is so much more outside for him than just getting exercise. He needs the stimulation of smells in the fresh air and all the different things to see.

I understand about Zeus getting cold, my miniature pinscher hates cold wether too. He will run outside to go potty then he wants right back inside. I put a doggie sweater on him and he's then fine, he'll stay out and plays a bit. If his feet are cold they make little dog booties too.