Not just that. You want to make sure the rest of the genes are the ones you want too.
IMO, don't really need to care about that first, because IIRC if mutation happened (the first time), all the genes would become the mutated bee type's gene (so your previous attempts will reset).
So you need to first get pure bred and then.. slowly change the gene..or use XBEE to change gene (easier and recommended) .. But first, breed lots of wintry bees to make sure you have enough drones for liquid DNA.
@vineet yes it's possible just make sure you breed the correct one i.e (A+B -> C) if you get hybrid AB princess, Hybrid drone AC and Pure A drone ; for the next time you might want to breed hybrid AB princess and hybrid AC drone.