V1 is an airspeed because it's airspeeds which are presented to the pilot, and airspeeds that he flies the plane to.
Headwind/tailwind is factored into calculated stop and go distances, so your V1 may change to rebalance the stop and go performance accordingly.
Another reason for using an airspeed not a groundspeed is that some parameters which determine V1 (such as Vmcg or Vmu) are airspeed driven, not groundspeed, and so a "groundspeed V1" would need to account for airspeeds anyway.