Sword of Spirit
Legend
5e encourages creativity.
Let your winter wizard take Fire Bolt only call it Cold Snap and change the damage type to cold. Similarly let the fire wizard take Ray of Frost and instead call it Hot Foot and do fire damage along with slowing the opponent.
Don't be so hung up on ONLY using exactly what is printed in the book.
Great idea! As a DM, I'd probably require the PC to do a bit of spell research for such purposes (and might adjust the effect slightly), because I like to think of the PHB spells as being the most commonly known spells, with most other spells being rare. But for some reason I had never thought of doing that to the standard cantrips.