Its often newbs have not figured out to ride toeside with their quads and knees...they don't bend their knees enough...sink down bend those knees. What you are probably doing is riding "tippy toes" to maintain toeside edge. Use your bigger joints and muscles, i.e., knees and quads instead of calves, ankles and feet.
While some of what you are experiencing could be chalked up to muscle fitness and endurance, a larger part is which muscles are doing the movements. Rather than applying the pressue through the ends of your toes, try pressing the whole front-half of your booth onto your toe edge by pushing the knee out and against the tongue and laces of your boot.
Yeah, I usually tell people that the hips are very involved. There are certainly pelvic actions that take place after bending your knees, almost like a pelvic thrust (no porn intended). But seriously, it is an all-body movement.
Also, if you're ever in the gym, I've found settings on an arc trainer (not elliptical, but arc - different machines) that hit the areas frequently used in snowboarding. Strong/durable abs are also key.