On rotations when we are considered "essential staff" (generally all of our inpatient months) we were expected to make it to the hospital, or to stay at the hospital if we didn't think we would be able to make it back to the hospital if we went home. They had cots and stuff set up in specific areas and would give you food and such.
During our outpatient years you just got a free day off if the clinic was closed for inclement weather. Didn't have to formally make it up but you did generally end up squeezing in a lot of people on the remaining clinic days.