I've begun carrying around a small bottle of Nutri-Drench (for sheep) and a 2cc syringe. I've found ewes who have 3+ lambs can't always clean the lambs off quickly enough, and the lambs get chilled. I stick my finger in the lamb's mouth, and if the lamb tests cold, I'll give it 2 cc of Nutri-Drench and check on it a few minutes later. The Nutri-Drench has a higher percentage of propylene glycol then other nutrition drenches that acts as an energy source, giving the newborn's "furnace" a quick start.
If that doesn't work, the lamb goes into the milkhouse where we have a simple system set up. We have a small electric heater, called a milkhouse heater, that stands about 15 inches tall, has 3 heat settings with a fan for blowing the heated air, and has a tip-over switch that shuts the heater off if it is knocked over. We stock up with empty produce boxes from the grocery store before lambing. When we have a cold lamb, we put the lamb in the bottom of the box and put the cover vertically over one end of the bottom so it only covers half the box....we put the heater at the open end so it blows into the back of the box and over the lamb. We have a thermometer stuck into the box and try to get it 100 degrees in the box.
Depending on the temp of the lamb going into the hot box, it may only need 30 min. to dry off and warm up. If the lamb is very hypothermic, it may need additional care....others will have to give the information on that since it involves injecting dextrose? into the peritonial cavity? (obviously something I heard about but don't do.) Sometimes the lamb is so weak upon being warmed it may have to be tubed and put back in the hotbox for a while.
The danger with taking a lamb away from the ewe is the ewe rejecting the lamb outright, or beating on it later if she doesn't remember having it and it doesn't smell "right." good luck, farming is never boring