Well yes and no!
Like most animals they are in tune with the seasons and during the winter month they will stop laying. It makes sense since any eggs that would hatch or young being born during the colder months would have a smaller chance of survival. This reduction in egg laying is triggered by the shortening of the day, less sunlight means less eggs.
While they naturally will slow down or stop laying eggs in the winter you can trick them by providing supplemental lighting. If you can provide 12-14 hours of light per day the quail will quickly return to laying every day. My recommendation is a simple string of Christmas lights with an inexpensive weather proof timer, both readily available at stores that have forgotten that we haven’t even had Thanksgiving yet, but I digress. These lights are weather proof, cheap to run (lower power usage), and easily hung around whatever cage you are using.
I recommend setting your timer based on your sunset time, meaning have the lights come on early in the morning to extend the first part of the day and go off either later morning or early afternoon. This allows the bird a more normal ease into the darkness of night as opposed to a sudden removal of the lights after dark and them walking into walls or something crazy. You don’t need to run them all day, just until after sunrise then they can go off saving even more energy.
Depending on your climate though you may need to collect eggs more often than once a day. Frozen eggs tend to crack and let in the bad bacteria. So make plans to collect at least twice a day or more if you climate gets and stays below freezing for extended periods.
Final thoughts – some people will say this practice is bad for the birds and they need to have a time of dormancy to recovery or it will shorten how long or how well they lay in future years. I believe to each his own. In my system I will use lights to keep them laying into winter and as spring time nears I hatch out new birds and replace all my layers with new stock. So I never know what I may be losing in future years.