Had my front bumper resprayed under insurance. At same time I got a new replacement OEM Aero Spoiler & had them paint that @ same time so paint would be perfect match.
Dealer that did the work advised me to wait at least 1 month before bringing car back in for spoiler install to allow bumper paint to properly cure - they would not warranty the bumper paint job if I did not do this, as he stated there is a high risk that the 3M tape used to attach the spoiler could pull off the new bumper paint if it ever needed to be removed if installed too soon...
This was during summer months here in PA.
You could still do spoiler install during winter as long as you have access to a heated garage & allow the car to warm up sufficiently, but you might want to wait till Spring anyway as flying road debris & salt on winter roads trashes the spoiler paint rather quickly - at least you'll have it looking great for one summer if you wait
Or you could also have the front bumper and/or the spoiler wrapped with clear 3M XPel after the paint has cured and never have to worry