A lot of specialty nurseries are very small operations (I should know.
Depending on what you are growing, and what the lead time is, yes you could be propagating your butt off right now. A lot of nursery plants are grown in greenhouses, where seasons don't matter, and are grown to arrive at the retail nursery at a specific time. The most obvious example is the poinsettia. Ever seen one in the nurseries in June? No. But the people that grow them know exactly how long it takes to produce the plant, and start their work that long before Christmas. A lot of bare-root tree growers are probably busing digging and cold storing their trees for Spring shipment before the weather gets too cold or the ground freezes.
So depending on what all they propagate, yes they could be quite busy.