As long as the ground is not frozen, you can plant anytime.

Hi samanthajade..welcome..welcome and Happy New Year!
As one who plants trees,shrubs,roses by setting the pot on the moistened,loosened(sometimes) ground while I decide where to place and plant it..(yeah, they root through the container holes) maybe you don't need my advice.LOL

But, I'd be inclined to pick your spots carefully and if you do dig to plant them better to dig wider than deeper if your soil is heavy clay.
Take the plant out of the pot and tease the longest roots free so you can set them in that wide hole.
Otherwise, left as is you get strangling roots and a plant that can tip over in bad wind or from ice storms.
Set your plants with the top of the rootball slightly higher than the surrounding ground for better drainage and oxygen to the roots.
That hydrangea wants a spot where it will get a sufficiency of water but it too appreciates reasonable drainage so choose your site with that in mind.

If you don't get them in the ground, at least scrape a depression to catch moisture and heel in the potted plants and draw some soil about a third of the way up the pot side. They want to be out and dormant.
Now, that's assuming they sent pots and not bare root plants. If bare root, you might want to pot them up and put them out heeled in with soil and mulch around them.

Don't think I'd do anymore business with a company that sends out plants that are leafing out in January that you were expecting in March.

Hi Samantha, and welcome to this neck of the woods. We also live in Cleveland County on the Kings Mountain side.