Do I need a neutral on the other end of a three-way switch?
No, you do not need to extend the neutral to all locations in a multiway setup

NEC 404.2(C) governs the provisioning of neutral at switch boxes (irrelevant parts snipped, emphasis mine):


  (C) Switches Controlling Lighting Loads. The grounded
  circuit conductor for the controlled lighting circuit shall be
  installed at the location where switches control lighting loads
  that are supplied by a grounded general-purpose branch circuit
  serving bathrooms, hallways, stairways, or rooms suitable for
  human habitation or occupancy as defined in the applicable
  building code. Where multiple switch locations control the
  same lighting load such that the entire floor area of the room
  or space is visible from the single or combined switch locations,
  the grounded circuit conductor shall only be required at one
  location.


The emphasized sentence applies to basically all multi-way setups you will run into in a house: it would be very strange indeed if you could not see what you are doing with the light from at least one controlling switch location.

Furthermore, the way multiway smart switches work only requires more conductors than fit in a /3 cable at the location of the "master" switch; a /3 is sufficient to connect the remotes to the master in all systems I have seen.