The original drain pipe was galvanized, and it cracked in the drainage portion? Then it probably failed due to rusting, which will not be an issue for plastic pipe.
As for freezing, the drain pipes shouldn't be holding water that could freeze. You should be able to keep your pipes in the exterior wall from freezing by putting high R-value per inch insulation (e.g. polyisocyanurate board) between the pipe and the exterior wall sheathing, and no insulation between the pipe and the drywall.
If your sink base is wide enough, and you don't mind exposed pipes with in it, the vent pipe could rise in front the studs, crossing over them at a 45 degree angle as seen in an elevation view, then turn into the wall on the other side of the king/jack stud, while still rising at a 45 degree angle (I think that would be a 60 degree elbow?), then 45 to vertical within the stud bay.
Or if your window is high enough, you could redrill the triple studs at a height 6" (or a little less if necessary) above the counter and stick with your 90s. If you have enough additional height above the hole, you could reinforce the stud pack with an HSS2 Simpson stud shoe, e.g. HSS2-3-SDS3 if the build up is 4-1/2" thick (3 x 1-1/2").
Or you could just stick with the noncompliant vent routing you have, even if it doesn't fly for new work, as it is existing and has been working OK.
Or you could install an AAV, and just leave the noncompliant vent hooked up in case it can admit rain water.
Cheers, Wayne