I would only assume railroad ties will hold up under most any type of weather conditions. My personal experience with concrete and extreme cold weather is limited being born, raised, and working in Southern California. This may be a question you want to ask your local concrete ready mix plant. I would totally recommend this type of hardscape idea for most any landscape and trust it would hold up under any harsh winters you may have in NH. As for the walkway buckling, you may have some drainage issues you want to address. I would also recommend using at least 2 inches of compacted road base and #3 rebar or wire mesh for reinforcement.
Good luck and thanks for asking.