Expecting to hoof it home on foot in a Winter storm is possible, but unrealistic.
If your car/ public transit isn't getting through, you probably aren't either.

Normal, unimpeded walking speeds are 2-5 mph. In a true blizzard, with high winds, drifts and very low visibility 1 mph would be good. Plus most of the roads and all of the sidewalks would be snow filled.

You would have to wear additional, heavy gear and:

And half of the time, its dark.
Being seen by cars and plows would be chancy.

In nearly every case, its better to stay with your car ( or move to a very nearby building)