I just found out how to keep Serana from equipping that hood of hers outdoors. I equipped her with some Legendary Darwnguard light armor and a copper and ruby circlet (it goes well with her eyes and hair). After that she doesn't put the hood on anymore. If I remove the armor, OTOH, on goes the hood.
Thought this might help some folk that wanted her to not wear the hood all the time.
Interesting, does she still wear the hood even after curing her?
Also, if anyone didn't know this, her hood is the only hood in the game that looks like that, that will not make the player look bald if they are a male vampire. Even though her hood uses the same model as the guildmaster hood, thieves guild hood, and Linwe's hood (which also make a male vampire look bald)