How did Alice get boots in the hospital?

At the top of the stairs was a coat-rack and, presumably just hidden from view, a shoe-rack with at least one pair of boots.

Since she had time to put on the coat before opening the door, there's obviously a very slight time-jump where she would have had ample opportunity to put her feet into some (laceless) mens boots before exiting onto the rooftop.

She may have come across the boots that disappeared from The Hunting of the Snark. Some people think that the Baker identified the Boo(ts) as the former vanishes, but I tend to think that the mysterious boots may have been found by Alice in this episode.