I would never spray a pasture. I tried turning some sprayed corn ground into pasture and it took a full 3 years before the herbicide carry-over was gone and the seeded mix would finally grow right.  I don't want my cattle eating herbicide.

On mowing/clipping or whatever you call it, there is no one-size-fits-all solution for all areas and systems. For example, around here the idea of stockpiling for winter grazing just doesn't work in most winters.

One basic truth is that cows require a fairly uniform amount of grass per day when grazing while grass growth is anything but uniform - more growth than the cattle can eat at times (spring-early summer) and less growth than cattle consume  at other times. This is where making hay or clipping comes in in many areas.

During spring grass growth, before cattle can get to it, grasses can shoot past the most nutritious state and send out seed heads which greatly reduce the palatability and  nutrition of the grass. Clipping it to keep it between the 4"-10" sweet spot height for grazing can be very helpful in some climate areas, like mine.

About how steep is too steep: I have my FWA 7610 tractor tires set out as wide as possible, front and rear. If I don't feel I can safely mow it with that tractor and my 8 ft, 3-point mounted flail clipping mower, I feel it is too steep for pasture and should be planted in trees or allowed to go back to being woods. Again jmho for our local, very hilly, SW WI area.