Much better to have condensation outside than between joists. Main reason to vent a bathroom is to get the moister outside, not odors, though that is a consideration. And better to have them outside too.
Can you run ducting, flexible dusting OK here, above sill thru rim joist or band? Or run between joists to place you can go outside? Maximum size hole thru 2X"X" joist is 1/3 width of joist, no closer than 2" from top and bottom. 3" hole thru your 4X10 would be safe, not so easy to cut. A larger hole 4" could be cut thru sill since it is supported along whole lenghth, a section could even be cut out as long as it is not under a joist or stud, and sill attached to foundation, plate attached to sill, within few inches both sides of gap. Attachment can be toenailed or wood, or better, metal "mending plate", sill and plate not going to lift, you just don't want them moving laterally
Flexible duct available in 3 and 4" diameters at HD. Rectangular ducts at HVAC supply.
Position outlet so "cheesy" condensation does not freeze on walks or drives. -20? Yall are nuts.Move to sunny southland where +40 is blood chilling and mild balmy summer days are 100+