Best not to sow carrots in freshly manured soil. They often grow in a "fork" shape then, so although their weight/volume might be OK, the useable part (after any peeling etc) will be less than it would otherwise be.
As far as horse-muck's concerned - as with any manure - it needs to be well rotted before you use it. These days more and more people are using wood shavings as bedding for horses (rather than straw) and this means it takes rather longer to rot down than the conventional straw bedding. I've used wood-shavings bedding from family ponies' stabling in the past - left it in closed plastic bags for 12 months though!