One guy works full time from at home because he prefers it and the project is setup in a way that we can accommodate him working at home.
Other people tend to work from home on a case by case basis. So if they need to be at home for any reason they can dial in - we're not precious about people being in the office all the time.
Having said that, the team largely prefer to be in the office, especially as they all live locally. If anybody else requested to work from home full time I suspect we'd create a company policy which was overarching rather than working on a person by person basis. Interestingly one of our strategic issues at the moment is finding enough office space to home all the new hires we've taken on recently. So allowing/requesting that more staff work from home might be a solution to that problem.
One company I worked for required everyone to work from home at least one day a month as part of the disaster recovery plan. It was neat that we could be fully remote. Made stuff like snow easy to deal with.