All of my girls (age five, three and one) have to be physically pushed out into the rain for busy!! girls are known to not like peeing in the rain. I have made dog coats from hand towels and ribbon to help with keeping them warm, flattening the fuzzy bits and protecting from the rain.
Fold over hand towel to correct length over the back and stitch in place, (so you can undo and re-stitch when they grow) piece of ribbon either side at the front to tie in a bow, and long piece to go round the midriff and tie over the top. cheap if you go to Dunelm mill or Matalan for the towel, adjust to growth rate and you can also use after a bath if you need to to keep them warm!!