I put mine outside at 3 weeks old (they were stinky and I was ready for them to move out of the house). I did put a heat lamp in the cage: my cage has walls on the back and sides, front is open (wire), but I hung a thick blanket over the front overnight and it kept them really toasty inside in 20s and 30s. Daytime (50s-60s) the blanket was off the front, but heat lamp was still on 24/7 for the first few weeks.
At this point (8 weeks old) they've been outside for some time and it's been pretty warm overnight (50s-60s), so the heat lamp came out about 2 weeks ago and they have just the regular light bulb. I do not cover up the front any longer unless it's an unusually cold night.
If yours are just coming out of the brooder, #StruckBy, then they will need to acclimate first because they've been in a draft-free warm environment thus far. I would suggest a heat lamp for a week (or two if it's still cold where you are) and cover them overnight and open them up for the day to get them used to the cooler environment and cool wind.
In general, you don't want quail in a drafty environment, so at least 1 corner of the pen should be boarded up to provide a hiding place from the elements. Each situation/place/pen is different, so maybe the best thing is to watch your quail: are they shivering and staying under the heat lamp? If so - keep it and give them additional shelter. If they are scattered, happy, sleeping away from the lamp - all good, take the heat lamp out and replace with a regular light bulb. Mine were scattered and pretty much not a single one was in the box directly under the heat lamp any longer and they were sleeping in boxes on the other side of the pen (not heated or lighted), so when I saw that - the heat lamp came out!
Hope this helps!