Generally, you need to phrase things in a way that benefits the company.
It's highly unlikely a conversation along these lines will get much interest from your boss. It also sets a bad precedent if they do allow a raise purely because you voluntarily move to a higher cost of living area.
Companies that have cost of living adjustments generally do this based on the company location, not employee location.
I would avoid directly asking your boss this.
Should I approach my boss with this?
What you can do is talk about your likely upcoming move and make mention of the higher cost of houses closer to work. You might be able to have this subject sort of come up naturally. Talk about how you want to live closer than 1 hour to work.
Once you've brought up the "we're thinking of moving to be closer to work" topic you also might have better luck if you mention the types of things your boss might be able to actually do to help with your commuting situation. "Hey, speaking of commuting, is there any chance I can X too?" Maybe you can work a 99999/99990 schedule. Or work from home a few days a week.
Once you are having a conversation about the subject, you could bring up a raise for moving closer casually. But don't expect anything.
You would have far better luck reading this question about asking for a raise and focusing on reasons you should have a raise other than where you choose to live.