I'd be suspicious of it even if it
is composted good and hot (since the outsides of the pile do not heat up enough). And I say this as both a gardener and as someone who has worked with horses (and the removal of the poo thereof) for the past thirty-some years
Although if you happen to have a source for manure from horses that eat ONLY alfalfa hay and pelleted food -- i.e., no grass hay (not even mix), no grain, no grazing -- that should in theory be reasonably weed-free.
There actually IS one way that I consider fairly 'safe' to use composted horse manure, if it fits with your particular gardening circumstances. I do this myself sometimes. The weed seeds in the manure will only sprout if they are near the surface (or are brought near the surface by your activities). It assumes you are starting a new bed from scratch, or tearing down an existing bed to totally-unplanted dirt such as you would do yearly in a veg patch, and are digging or double-digging the whole bed anyhow.
So, if you find yourself in that circumstance and have some composted or at least semi-composted horse manure you are dying to use, you can load it into the bed in a deep layer, on or instead of the top of the subsoil, and make sure it's covered by at least 8" of regular topsoil. Then you must
never rototill or re-dig it the bed (nor make deep planting holes, although in that case any weed sprouts would at least be very localized). Then the composted manure can just sit down there providing a nice rich retentive lower layer for plants to dig their toes into. Most weed seeds will never get light to spur them into germination, and the ones that *did* get triggered to germinate when you were putting the manure in place will be covered by so much topsoil they will poop out before reaching the surface.
But be warned, if you dig this bed over some years later, all bets are off. Most weed seeds can sit in the soil for a really
really long time before exceeding their 'best by' date
Me, I put my composted horse manure back on the pasture in spots that need soil amendment. It's useful, it's closer to the barn anyhow, and I can easily live with weeds
there
Pat