You can take the same protocol, just begin with fixation of the frozens in 36% formaldehyde or methanol for a half a minute, rinse with tapwater and go on with hematoxylin. The main difference is, that you don't need the steps of deparaffination and rehydration.

Does the Methanol need to be ultrapure?

No ultrapure Methanol is needed.

Do I need an aqueous mounting media?

If you dehydrate and clear your slides after HE you don't need an aequous mounting media. Dehydration is preferable, because eosin would bleed out in aequous media.

Frozen sections after air drying can be fixed,washed and stain with haematoxylin , (washed in tap water), dehydrated and stain with alcoholic eosin (wash excess eosin ) dehydrate ,clear and mount in euparol. Aqueous eosin can be used instead and then sections can be mounted using glycerine jelly .