How long are these outings going to be? Dogs in general do well in the snow and cold, but a four month old won't be able to do too much, and may get chilled as they just don't have the body density to keep their body temperature up.
I go snowshoeing with my dogs all the time, but they are adults, used to the cold and snow, and I'm only gone on two or three hour outings. (They could do more, but that is about all I can do).
BH, OB1, TR1, AD
Rottweiler/Hairy Dog mix?? Shelter rescue
Gryffon Vom Wildhaus