On a student/beater bike budget, use decent brake pads. Clean the crap off your rims. Feather the brakes to remove water. Slow down and look ahead. Fit some quality winter tyres if you are running crappy ones .
Drums are consistent in the wet, and dont ice up as much (Q: do they ever ???).
Disks need a beefy fork with special braze-ons. Cheapo MTB disks are underwhelming compared to decent road caliper brakes.