I'd like to think most folks know if they can or can't walk 15 minutes, so I'm confused at the question. Rain is easy, get a solid rain jacket and a raincover for a backpack. Cold, a good raincoat is essential for just walking around NYC let alone a walk to the train. Snow, that's the tricky one.

I did a few years living on West Side/Communipaw and that was a like 25 minute walk on a good day. It was fine most of the time and cabs were cheap on the super rainy days. I'd cab late at night if I had been drinking, but I'd say 99% of the time I was walking rain, snow, or sunshine. I moved downtown and really enjoyed getting some time back with a 5 minute walk to the train, but to get the 5 minute commute I had to give up a huge apartment with a backyard and trade for a small apartment - it's really all about what you value in your life. Now I'm in Brooklyn but bike everywhere no matter the rain or the cold, so maybe I'm a bad judge on commuting in inclement weather.