Hi, Sarah, welcome to the forum.. Glad you joined.
Where are you located? That might give us a clue what you mean when you say nights are turning cool. I don't know if you mean into the 60's Fahrenheit or well below zero. Just how important is it that they do sleep upstairs? If you modify your profile to show location that information is always available. That information can come in handy for many things, not just climate.
Thanks for including that they are Silkies, that helps. Silkies cannot fly. That can make them a little more challenging than other chickens. They can jump and walk up certain slopes but getting down just might be more intimidating than going up. A lot of times they can do things but just don't want to. What reason in their mind do they have for going upstairs?
Not all Silkies roost either, sometimes they are quite happy sleeping in a low spot. If they do roost that might be a reason for them to go upstairs. What does the inside of that coop look like? As small as it appears to be based on the nest size the roost is probably pretty low and accessible but maybe not. Could you possibly post a photo of the inside of the coop?
That ramp may be a bit steep. Is it attached in a way that you can put a block or something under the low end and flatten it out some? They could hop up onto the block and then go up the ramp. Or maybe add a couple of cleats across it to give them a better grip with their feet. Or maybe replace it with steps. They are bantams so maybe steps 6" high, 6" deep, and about a foot wide should work.
If you want to train them to sleep upstairs the best way I've found is to go out there at night after they are settled down to sleep and lock them in the upstairs coop section overnight. Not sure you can lock them in there but hopefully you can. I've been through this with elevated coops before. Sometimes I only have to lock them upstairs once and they learn. Sometimes it may take 3 weeks before they are all going upstairs on their own. Be patient and consistent and they should learn.
As small as that coop appears to be I'd be down there pretty early the next morning to let them out, at least for the first few mornings until you are sure they are OK together locked in there. They probably will be OK locked in there, but it's a reasonable precaution I take when I first lock mine in overnight. Usually it just takes one or two mornings before I'm comfortable leaving them locked in there until later if I want to sleep in. The next morning I'd just open the door and walk away. Let them get used to finding their way down.
If you can you might try setting one or two of them on the roosts when you move them upstairs. You may not have good access. I don't do that, I just lock them in and let them work out where they will sleep, but if you can get one to start sleeping on the roosts that may keep them from sleeping in the nests.
Good luck with it. Lots of people go through what you are seeing and it is not always with Silkies. Just because the others can fly up doesn't mean they always want to.
