In reply to Roberttaylor:
400 or faster, because handheld. 100 if the light is good and the lens is fast and/or you don't mind shallow depth of field...
Make sure the camera, if it has manual speed setting options, is set to auto-read DX codes on the film, just in case you change films.*
Your options are about 400 and 100 in B&W, and a few more in colour. 400 in C41 B&W (Ilford XP2) in snowy conditions will give you very smooth results but actual true B&W will look nice in bad weather because of the 'graininess', IMO. XP2 is fine grained, so there might not be a need for you to use 100 much? The true B&W films at 100 can be very fine grained, however, should you want enlargements later.
Colour 400: Kodak Portra films can give nice natural colours and this can actually look ok in brown, green and white winter shots in the UK hills. Kodak Ektar 100 will give you more punchy colours. Portra 160 is nice and probably somewhere between. There might be a supersaturated Kodak, and Fuji, colour film where you are going, for much less money and these will make dull days seem nicer. Poundland actually sells something like that I think but you only live once. The benefit of the Kodaks is that they are very forgiving of over/under exposure and are slightly more technically advanced, though taste is everything. There are some 800 speed colour films but I doubt you will need to pay that much and risk the grain for what you are doing.
Slides will mean using filters because of the blue light and really only if you want a slide show, though they can be spectacular. 400 slide is a bit rare these days, I think?
Do you have lens hoods? Screw in ones can be had cheaply on the usual auction sites. I think they are essential.
Jon
*If you can adjust it manually, you can play around at pushing (or pulling) speeds later on, especially if you develop your own. If you only have auto DX then you can still get there by using stick-on DX labels or scratching off the relevant bits of black paint.