Instead, keep animals warm by draftproofing their sleeping areas. If you close applicable doors and windows and it still seems drafty, secure a plastic tarp around the stall or jug where sick animals or newborns are kept. It isn't elegant but it works!

Then, deeply bed the sleeping area with straw or hay, not shavings or sawdust, so animal(s) can hunker down into the bedding for additional warmth. 

And if it's really cold, blanket them. It's easy to sew your own lamb, kid, cria, calf or foal blankets or craft them from clothing from the used-a-bit shop. For instance, for many years we kept winter-born Minnesota foals toasty warm with children's wool sweaters and goosedown vests from secondhand shops. Goosedown vests are easy: simply feed the foal's legs through the vest so that it snaps along his spine--that's it! Using a wool sweater, trim off the sleeves and fit it on the foal the same way. 

Dog sweaters fit small species like lambs, kids and alpaca crias to a "T". In fact, acrylic dog sweaters (they're very stretchy, so easier to put on a baby animal than you probably think) are ideal when it's too warm for a bonafide blanket but it's a tad too chilly to go completely without.

And many seamstresses market blankets tailored for specific species. Keep in mind that kid and lamb coats are interchangeable and blankets that fit foals will usually fit a calf (if it's a male calf, make certain the foal blanket isn't constructed using surcingles or bellybands that will cover or rub his penis).

Do make certain coats and blankets you put on your animals are safe. They should fit, not hang so loosely that the wearer gets his legs tangled in fabric. 

Here are some resources to help you get started.

Make your own

Maxine Kinne’s great sew-it-yourself goat coat instructions

(these would work for lambs, crias, foals and calves, too)

http://kinne.net/goatcoat.htm

Make a lamb or kid coat from an old sweater or sweatshirt

http://www.bellaonline.com/articles/art35572.asp

Make a lamb or kid coat from old sweatpants

(construction information is near the end of this good article)

http://www.dairygoatjournal.com/issues/85/85-1/Nancy_Nickel.html

Custom made for your baby animals

Pat Canipe makes the BEST custom-made kid, lamb, cria and foal blankets I’ve ever seen, bar none!

(my goat baby Uzzi loves the fleece-lined, ripstop nylon kid blanket she made for him)

http://www.custompetandtack.homestead.com/index.html

eBay is a great source of readymade baby animal blankets too:

Goat blankets

http://search.ebay.com/search/search.dll?from=R40&_trksid=m37&satitle=goat+blanket&category0=

Foal blankets

http://search.ebay.com/search/search.dll?from=R40&_trksid=m37&satitle=foal+blanket&category0=