Welcome fellow Canadian! Do you have a name for your bully yet?
It's really cold here in Toronto as well, so we're avoiding taking my bully, Stig, out. I guess time and patience is key, give a lot of encouragement as well. I know a lot of bullies who work for treats no problem. He also most likely doesn't like the weather, so you may have to keep on doing what you're doing until it gets better. There are a lot of bullies here in the forums where they avoid snow and the cold altogether and rush back to the house whenever possible! Because my bf and I work full-time and sometimes have to leave Stig alone in the house for 7 hours, we trained him to do his 'business' at a corner in our house, which he does really well on. We don't mind the clean-up, but you may prefer the alternative.
A lot of owners here also prepare the bland diet for their bullies. It consists mainly of boiled chicken and rice. It's easy on their tummies and they all seem to like it. Fromm's a great choice, by the way! You can also add in healthy treats such as frozen green beans, carrots, etc. Yogurt and canned pumpkin are favourites as well. They're great for digestion issues.
Thank you for taking him in. And by the sounds of it, you're already a great owner! As you may read from other posts, we love pics!