cold air is perfectly fine you just have to not get close to the "dew point" otherwise that will be where the air gets saturated and then you'll have moisture problems...
that is if the air is also being passed through filters etc... and 250 cfm may not cut it as far as movement is concerned if you have filters going through...
it might cause the cold air from settling too much in your ventilation ducts...
if you use one main large scrubber this shouldnt be an issue as if you are feeding the hot air back into the house then just check that there is plenty air pressure coming out and you should be okay