Mini Horses
Herd Master
For horses, just bringing a stallion on site will often bring mares into estrus. (Goats, often a stinky rag for the does will work!
Ahh trailer rides! When a horse is showing colic signs, first thing you can try is a trailer ride -- 99% of time they poop for ya.
At shows, winners are often required to have a pee test for horse to check for drugs. Take them into a clean stall and within minutes, they will oblige and pee. Animal habits!You are doing great! keep a good, deep layer of hay/straw for them to snuggle into. Keep the heat lamp high enough to prevent burns, fires, playing with it by the goats. I'd set the timer to start the cycle about 10-11 PM.....Stop cycling about daybreak. That covers the coldest of the night, enough to temper the cold and not "heat" their area beyond hair growing. 5 weeks is still young, I thought they were 8-10 weeks for some reason. That extra month makes a big difference.
Check to be sure the area they are in isn't drafty...you want air flow in their barn but, not drafts at laying in the straw levels. I've had to add a solid board across some timbers sometimes to hold off wind blowing in small areas where wood may overlap. Doesn't have to be heavy wood, just solid. Don't use plastic, they will chew and possibly eat it. You know how kids are!
You may want to look at adding a Wide "shelf" of solid wood above their favorite laying area...helps contain body heat they generate in their own area. Now, THAT has to be heavier wood because they will jump on it during the day. Goats are regular gymnasts.
Just thoughts that might be helpful/doable/easier in an area where there is far more cold than those of us in VA & TX & FL will see.
In case these are helpful to keep things warmer.Reading more of "how" you bought them --- YES in your area, too cold for them at that time. If you get more very young be sure to ask if they received colostrum! That's the first milk (in case you aren't thinking about it right now) which gives them antibodies and super thick, sweet, enriched for a good start in their gut. No colostrum, big issues often. Hey, at a diary she can't use that first milk for anything else. Get a couple quarts to bring home And that isn't much for her because my Saanens have fed trips and STILL given me a gallon of it! They are heavy milkers. You never MW it! Refrigerate and heat by putting in a bottle, setting in hot water to warm, then feed. It can be frozen, thaw in frig, heat as above. Just something that crossed my mind.
PLUS buy Spring or early summer. 
They probably did get colostrum as typically a dairy pulls the young and bottle feeds all. They generally use a lambar. And generally watch/help to make sure the kid gets to using it. That's just generalization FYI.
mood to kiss and make up 
and everybody is friends again. 
