I almost never use a heat lamp unless I have a sick baby. Ok, maybe if it was below freezing then I'd probably use one for a newborn for the first night until I was pretty sure they could maintain their body heat. They do pretty well in the cold weather if they are dry, draft free and have some good bedding. I think your little gal will be just fine!
We get that damp cold too. Just check on her...if she's shivering and hunkered up ...the lamp would be warranted - but likely she's not going to with an outside temp around 50ish and a full tummy.
Plus, they like to snuggle with mom...more heat. I am so very, very, very happy that this kidding went well!! Yes, she looks a lot like mom and that ain't at all bad.
First kiddings can be quite anxious but what you had was a sad, unnecessary disaster. Now, a new life begins -- enjoy!!