What I would do is dig out a spade and a half depth of soil from the veg patch, add the manure now, then place the soil back on top. You will have nice deep fertile soil that will have rotted down by spring that will not sprout any weeds.

Another option is to put the manure on top now then place wet cardboard down on top of that to stop any weeds. The cardboard will rot down over winter and you can fork in the remnants in spring before starting planting.

Both good suggestions Kildermorie

I have my horse manure in a heap under a shelter. It will heat up and kill any seeds.
Dont worry if it steams.
Marvellous stuff ! You are very lucky. I drive to a farm 15 miles away to get mine. The daughter keeps 2 cart horses as pets. The wood shavings are used when a horse is sick and has to be kept in the stable, they take 2 years to rot down, but are ok to dig in on the land.
I grew Picasso Potatoes, got some tubers that weighed 2.5 lbs.

here here kildermorie .

In answer to your question ... yes, if you bury it deep enough in your compost. It needs to heat enough to stop any weed seed from sprouting. This is difficult to guarantee. Well-rotted horse manure is wonderful but it needs to be worked on before it can be safely weed free and used. I suggest a cover over the compost of carpet, holed plastic etc to keep out light but allow other elements of air, wind and water to penetrate.

If the horses have been fed on haylage weed seeds will be minimal. Unless you have a very high temp compost Avkg any weed seeds within are likely to survive, not just ones in horse dung. Personally I'd go ahead and follow one of Kildermorie's has suggestions. As this is going into a vegetable garden the weeds, if any, can easily be removed by hoeing.