Captain reported a high workload led to the flight crew missing the restoration of engine bleeds; leading to a pressurization issue until it was recognized.

Narrative

The weather was much worse than forecast. Wind gusting to 50kts. I attempted the ILS. We briefed and set up for a wind shear landing (bleeds off; props 1020). I was unable to keep the aircraft on a stabilized approach; and conducted a miss. In the subsequent miss; climb out; call approach; plan a return to ZZZ; call Dispatch; talk to the flight attendants; and talk to the passengers; we forgot to turn the bleeds back on. Climbing thru 10;000 ft; the master caution 'cabin altitude' illuminated. We knew immediately what the problem was; ran the checklist; and restored pressurization.This was an extremely difficult approach that had both crew members taxed to their maximum. With all the procedures to follow; and still try to fly the aircraft safely; it was simply task overload; and switching the bleeds back on during initial climb out got missed. We were able to restore pressurization quickly; once we had the time to deal with the issue. Lessons learned; go slower; and more methodical regardless of the situation. Make sure each item on the checklist; or flow is accomplished.