the hosta can be left in the ground, it is perennial meaning it comes back each year. (dies to underground in the winter, regrows).

I am not sure about the sedge, I usually think of sedges as swamp grasses. I don't imagine there is much to do with it.

The hosta can be dug up and divided once it looks like it is getting big. (probably once every 2-3 years) You just chop the roots of the plant in half and replant and then you have 2 hostas.

The sedge you might try checking to seed if it has seedheads. If they aren't eaten by the birds you can store them overwinter once they have dried on the plant and try planting the seeds in the soil come spring to see if they will grow more.

There are jillions of ornamental Carex (sedges) so we would need a picture to help you give it a real name. Many of the sedges are extremely hardy, but others are not. No telling about yours without a species name. Hopefully he purchased it at a nursery that only sells plants that will be expected to survive in your area.

The hosta will be killed back to the ground with the freezing weather, but will come back in the spring.

The Sedge retail stake says "Carex Comans Bronco"

I also have another plant out there (link below) that I haven't identified yet. When it was first planted it had peachy colored blossoms but I haven't seen blossoms since around May. Any ideas on what it could be and how to care for it during winter?

Thanks! The tips so far have been most helpful.

Here is a link that might be useful: {{gwi:1061304}}

Some sedges keep color in their foliage all winter, others die back to the ground. Don't panic until next spring if the sedge disappears!

Hosta are usually one of the last things to come up in spring, so don't worry about it and think it died, just wait for it.

Your ornamental grass, also called 'Leatherleaf Sedge' is reported to be hardy to -10 deg. F. Your other plant looks to be one of the Satsuki azaleas, can't say for sure without seeing the bloom. Azaleas flower once per year, in the spring (early to late, depending upon the variety).