Hi Kate,
I grow pumpkins and gourds. We live in the land of red clay, in SC. I fortify my garden spots with a mix of horse, chicken, and rabbit manure. It's all dried and crumbled well, and I just mix and mix it into the soil.
As for cow manure, make sure it's well dried. Pumpkins have the 'sucker roots", as I call them, all down the vine.
I believe, if you crumble it up good and sprinkle it under the mulch it will be beneficial. I wouldn't get it too heavy, though.