So you have vertical Dropouts? so 1 speed , you have a chain-tensioner ?
How about a SA 5 speed IGH, Drum brakes work well in foul weather , but will blow past your stated Budget.
35 wide studded tires.. Drum -dynamo front for lights without batteries
Flat lands,, You can fit a dual drive rear hub and a straight block cassette , like a 12-23t
with the 3 speed internal offering a quick downshift at stoplights..