i always thought wellies were rubber boots, but not over boots. (you slip your stocking feet into wellies, and old ladies wear them in the garden, and step out of them at the garden gate, or back door, and put on shoes or slippers.)
galoshes, are over boots... as Mav rightly points out, they had latches (that would only latch when warm, but once you trudged through the snow, and the metal was cold it would contract, and be impossible to open again or latch.
most women now were leather dressy boots, in the snow.. not welly type or galoshes.
