I have a finished basement with a small boxed-in corner section where the water supply enters the house, and an outside tap is run. I just replaced it over the summer but couldn't use frost-free because the box just isn't deep enough so I have a ball valve outside and a nice little stopcock inside with a drain plug.

I have had a pipe freeze up in this box once, it's not well insulated and there's just vapour barrier - no drywall inside, so clearly I have to deal with those first.

What I'm debating about is at what point is it wise to insulate the (copper) pipe itself? Clearly within the insulated envelope it needs to be insulated, but my thought is, once inside the warm part of the building I need to leave it exposed to allow condensation to evaporate and the pipe to warm up as much as possible...

Part of the cold in this boxed-in area is from poor insulation and sealing, which I'll deal with. I've also got the inner covers removed so the household warm air can get to it.

The other transmitter of cold is the copper pipe itself, from the outside tap in. To deal with that, I plan to wrap a heat tape around that section of pipe (and for that I do need to insulate the pipe, according to the instructions - I already have a GFCI circuit run there ready.)

So I kind of think, expose the pipe wherever possible within the warm side of the envelope, with the exception of the area under the heat tape.

I also wonder if I should ensure there's a vent to allow air to circulate inside this box once I make doors/covers to conceal the pipes. I'd prefer not to, so I can reduce the pipe noise (another reason why I'd be tempted to sleeve the pipe - clearly the water's warm enough on entry to the house, it's the cold around the outside tap.)