If you run the hose on contour it
should not move as much, and if you anchor the hose by looping it around tree or hooks/pegs in the ground it should not move much.
You could also bury the pipe a inch or two. Also sub-surface water is the best type of water, followed by on ground drip type irrigation, the worst is sprinkler/sprayer types.
The idea of water a pasture, doesn't rest well with me.
It seems that your problem is that you want more greener grass. Watering is only one possible solution
Have you tried rotational grazing, swales on contour, planting more nitrogen fixer/aka fertilizer.
Maybe you have to use animals more tolerant of our location.
chicken vs duck, goat vs cow, or just a less picky cultivar/breed.
Reseeding the pasture with more drought tolerant cultivars/species, you may have to reseed twice a year one for summer "grass" and another for winter (winter rye).
Here is a pasture list too.
The main thing to remember is that you want 4 types of plants 1.N-fixers, 2.Drymass, 3.Pest control/medicine, 4.Aerating
roots
I would plant 7-12 plants in each category.
mustard
burdock
alfalfa
lamb's quarter
fava bean
sweet clover
lupine
landino clover
buckwheat
hairy vetch
daikon
black-eyed peas
comfrey
sun flower
yarrow