Re: My first winter....Care questions.
i just checked the weather for salt lake city and it's way to cold to have syrup in the hive.
the bees can't take the syrup when it's much below 55 degrees. having the syrup in the hive will make it colder in there, and it could add unwanted humidty as well.
i would take the feeder off, and try to figure out how much honey is still in the hive. it is better not to feed them unless they are going to run out of food.
one way to check stores without pulling frames is to look at the top of the frames in the top box, and see if you can see any capped honey.
another way is to see how much your hive weighs at this point, and compare that to how much the boxes and frames would weigh empty.
welcome to the forum timco.
disclaimer: novice beekeeper here who knows just enough to be dangerous