Can you encourage a hen to go broody? Yes, but encourage is all.
Here is what I do, it can work but it does not have to, you cant force them. I do all mine in private quarters (bachelor pads), to do this I put a nest box in the pen (in plain full sight of all the flock), and put a golf ball in it. The girls will inspect as does the rooster, and may start using it. If/when they start using it, I take the eggs and replace with 1 golf ball, or maybe 2 if several girls use it. When the balls add up, and the girls do count them, one just may set on them. When this happens, at night I take the golf balls and replace them with the eggs I want hatched. Once the chicks are hatched and moma is ready to bring them out, I open the door so she can come and go as she pleases. At about 4-5 weeks she will take them to the roost. She may also move to a nest in the coop for nights at some point, it is her choice.
Does it work every time,, no
And there is nothing wrong with winter hatches, yes it feels wrong to see 3 day old chicks out in the snow, but moma is right there and they can warm them up anytime they want.
Good luck!