First time growing Tomatoes from Seed in Greenhouse, after Pricking them out, will growth of Roots be ok, in 3" pots until after Frosts and putting them outside.
Generally yes but it depends how big they get really, once the pot is full of roots they need to move on otherwise they will receive a check in their growth, it will also become very difficult to supply enough water
If it is assumed that they will be planted out perhaps at the end of May, or beginning of June, then they could need to be moved up a pot size, eg 12cm so that they can continue to grow unchecked ...
I have mine in small drinks cups until they are about 4 inches tall, then pot them up ready for planting out.