I personaly would never mulch with cow manure rotted or not. There are so many different seeds in it that you could possibly cause your self more work then before. And if you happen to get some that's not completely rotted you could end up burning your plants. I see cow manure good for two things. 1 compost or 2 working into your soil before planting.

It is a good soil amendment but not really a mulch. However if you compost it first - mixed well with several other ingredients - the resulting product is called manured compost and can be used as a good mulch. There are other better mulches but they don't add as much to the soil as manured compost will.

Generally "well rotted" means 4-6 months so in your zone there is plenty of time before you'd plant. You could spread it over the garden area along with layers of other materials and just let it compost in place there. Till it well in the spring and it will be safe to plant in then.

Dave

As a cattle rancher , I use cow manure as a compost ingredient and as mulch . Cow manure is one of the least seedy manures around .
It is a great ingredient for firing up a compost pile .
The only way to know what will happen if you use your own cow manure is to just go ahead and use it in different settings .
There is no rule . We learn through trial and error .
Be cautious if you are concerned about the outcome of your trial plants .

Manures should not be put on, or in, a garden unless it is composted first. So no, cow manure would not be a good mulch on a garden.

"I have no idea if cow manure left where it was deposited for several years, dried to grey on the top, but rich brown underneath would be considered rotted at all."

Nope, it's dehydrated cow manure. Compost it before using. My "mulch test" for my food garden is that if I can drop food on it and still eat it (maybe brushing it off first, maybe not), it's ok to use. Manure, even dehydrated, does not pass this test. It's still poop.

Hmm, mulch in Wyoming. Straw is a great mulch. Any tree trimmers in town? Or get a chipper-shredder? Is it too late to start a cover crop?

Otherwise, yes, you can use compost as mulch, if you can't find anything else and you have enough to spare. The grass would be ok if it's dried out; you wouldn't want to put globs of green grass around your plants -- could get hot or slimy. A small concern, if you're using the lawn clippings to mulch a food garden, is that people may have used chemicals on their lawns.