Hi & welcome! To assess this, check the hardiness of the plants in the trough. The general rule is plants that hardy to one zone lower than your location are generally safe to keep in a pot all winter. Do you know what (gardening) zone you are in? You can check it here through this site:
https://garden.org/nga/zipzone...
Then you can research the hardiness zone rating of your plants. For example, if you are in zone 4, plants that are hardy to zone 3 should be no worry. Plants that are hardy to only zone 4 could be iffy but I think plants purchased as perennials for your location would likely be OK in something as substantial as a horse trough, even if they aren't hardy in the next zone.
You can increase the insulation factor of the trough by surrounding it, particularly the sides, with something like leaves, straw, blankets, whatever you can come up with to buffer temperature swings which are more pronounced for a container. Adding a layer of mulch, leaves, other available organic matter over the soil surface after the plants have gone dormant can also help. I would try to add enough so that the surface of the material in the trough is at least as high as the sides, so water can't pool in there and cause the trough to be more soggy than the surrounding soil.
There is a plant database on this site but it doesn't have hardiness info for every plant.
https://garden.org/plants/
If you need more help, please let us know your zone and which plants you are unsure about.
