Should I try to limit my boyfriend's smoking
Good idea! How do you plan on doing so because it's going to be hard to quit smoking.
It's not like I can force him to quit, but I can make it very difficult for him to smoke outside.
That sounds like a good plan!  Trying to help your partner cut down on smoking is a good a and shows you care about their health.  I hope it works out!
I also gave him an ultimatum where he had to continue our relationship or his smoking.
You are really nice to try and help him quit the nasty habit. Sometimes it takes tough love to make things happen. He will probably quit because you are too valuable to him to lose.