Possible Clues:

• Cupid, e.g.
• It sounds beastly wet, my love
• Animal that pulls Santa's sleigh
• Beast gets on home beside two rivers
• Check noise made by pet caribou
• Check the animals are ones inured to cold
• Animal from 1 across
• Sounds wet, my darling, for Santas Claus
• Control over reed for antlered friend
• Cats and dogs, darling, are noisy animals