So I’m a beginner in bonsai. I have a juniper which I understand can be indoors year around even in winter (I live in Missouri). But what about Chinese elm? I’m not putting it outside now due to it recently being in the single digits temperature wise. But for next winter, do I bring it inside when it gets 15 F and lower? I don’t want to shock it I’m just confused. 

NO you CANNOT keep Junipers inside!!!! Get it out now. Chinese Elms also will not survive long inside. There is no confusion, Chinese Elm are totally hardy to -5C at least. Junipers ever lower. Whoever told you that you can keep Junipers inside is an idiot, and knows nothing about trees.

You need a cold garage or shed to keep them in if it is very cold

My chinese elm endured six weeks of temperatures below -10 night and day. Record low was -18 during that period. It not just made it true, it growed better than any year the summer after. Not that I want to recomend a beginner trying, just want to elaborate on that they can be more hardy than most people think.

I had my junipers out in that coldspell as well. For junipers I can confident advice a beginner not to be afraid of temperatures above -10. This species grows naturally in alpine conditions as well as cold temperate regions. I have seen several growing in gardens north of the arctic line.

BTW, I am in western Sweden USDA zone 7, but very wet winters. I quickly read up on minesota climate, I think the trees will be fine. Put them on the ground in a wind sheltered area and cover with snow.

Woah, any tree inside (except very few circumstantially) is a big no-no. I had to learn the hard way as well. I keep my dwarf jade inside under a grow light but that's not even a tree, it's a succulent.
It doesn't get very cold for very long where I am, but my juniper and umbrella pines do just fine in freezing temps with just a towel tucked around the pots for extra insulation. If you're still worried about your juniper you can do that to ease your mind but I believe they don't need protection until 15 °F or -10 °C.