I always understood that Whitsun was the correct season for Morris, and that Headington were dancing out of season when Sharp discovered them.

But here is a reference to Morrice at Christmas from around 1680, in the Bodleian collection:

The Morrice Dancers will be ready
Meat and drink enough to lade ye
And in a fools dress will be little Neddy
To entertain our Christmas Lady

So were the academics wrong all along?

The Shrop-shire VVakes or Hey for Christmas