Re: New beekeeper here! Help overwintering a weak hive in Boston?
You can feed 2:1 syrup as long as the temperatures remain above 50 deg, at 50 and below the bees start to cluster and will not take syrup. For a future reference fall feeding if needed should start in September in your neck of the woods, however at this point in time if you can see some good weather ahead on the long range forecast then keep the syrup on the hive and let them take as much as they can. If your weather is starting to turn off cold it would be best to remove the feeder and place granulated sugar on the hive, this is done by placing a couple of pieces of newspaper on the top of the frames then pouring a bag of granulated sugar on the newspaper, if you have an inner cover place it back on the hive with the deep side down to provide a little more room for the sugar and you will need to check on them from time to time during the winter when the weather permits and add sugar as needed. This sugar provides an added benefit of absorbing moisture in the hive.
The suggestion of moving them to a shed is a good idea but I would wait till the temperatures drop into the twenty range and stays there for a number of days or your forage bees will return to the original location where the hive used to be. Bees have about a three day memory so if the cold keeps them in for at least that long of a time they will reorient to the new location. There are methods of placing tree branches and so forth in front of the entrance to force them to reorient to the new location but I would suggest to just wait till it gets colder.
Bill...in Southeast Ohio Zone 6A, Never look down on anybody unless you are helping them up