The paper can't get any denser than it's full black, and that's achievable via enlarging or contact printing, assuming you're using the same paper. Contact printing, on it's own, won't change that.
But, to address your question;
If you metered the snow and didn't compensate on the exposure by opening up 2 or 3 stops, then your negative may not have enough density to render the snow near white in a "normal" print. You might need to heavily dodge the snow to get it white, and perhaps filter for more contrast, or use a harder grade paper, in addition to dodging the snow.
If the snow areas in the negative are sufficiently dense to render the snow near white, then you may be over-exposing the print.
Getting snow rendered well is tricky, and it has all sorts of shades depending on the lighting, it certainly isn't always white.