If you got no snow, a tall central pole well-set in the ground and topped with a tire, with 2x4s or strong cable going out to your run fence (or beyond) like the spokes of a wheel only slanted downwards from the pole to the run fence, could support a large piece of aviary netting. That would probably run you into the $300+ range but would work, except perhaps if very high winds were a problem.
However with snow load involved there is really not a lot you can do that won't cost a LOT, and still have collapse under snow load be a concern. Any material you use WILL catch significant snow (at least when it's a wet snow) and sag/rip unless very very very strongly supported at close intervals.
Have you considered just building areas of cover in the run so the chickens are never too far from somewhere they can duck underneath to get away from a hawk? Brush piles, little table-shaped or a-frame things (someone here uses pallets wired together as a low 'A', which sounds quite sensible to me), etc. That would be far more feasible.
Good luck, have fun,
Pat