I'm in upstate NY, too.
I wouldn't move your bees just yet, but when you do, it will be uncomplicated.
The reason not to move them yet is that we are still having very cold weather for another couple of weeks. If you bust up the cluster in temps when it's marginally too chilly for them to rebuild it before they and their brood get chilled, you can do substantial harm to them.
And if you move them, even with elaborate re-orientation precautions some will wind up back at the old location, and in chilly weather they may not have enough time before they become fatally chilled and die.
So I'd wait until at least April (unless you are on the lake, or really your "upstate" is really downstate in comparison to where I am north of Albany.
By far the easiest way to move the hive is all strapped together in one unit. If you can take a box off that isn't needed for the day or so around the move that will make the hive lighter and easier to move. If not, that's OK. The easiest way to lift a whole hive is using a chain wrapped around the bucket of a tractor, with a hook that attaches to a pair of ratchet straps used for the hoist. With an additional pair strapped tightly around the hive, that are there solely to keep all the boxes rigidly together. The double-pair of straps (4 in all) make the move secure and easy. My husband moves my hives around all the time this way.
You can also move them on a hand cart, or something similar.
If worst comes to worst, you can even move each box individually (see Michael Bush's instructions on that). I did that at first but found moving the whole hive in go so much more satisfactory that I no longer use that method.
What I have adopted from Bush's instructions is the idea of what I call the Left-Behind box. Simply put it is deployed in the late afternoon at the old place to collect any late-day stragglers who can't find where they started from. The after dark it is carried back to the new location. I have also modified the original instructions which called for setting the Left_Bind box nose-to-nose with hive an hoping the bees transferred themselves in side. Now I place a bee escape board under the cover of the hive BEFORE I strap it together for the move, and leave it in place after it arrives at its new location. Then when/if I collect any strays in the first few days after the move I need only pull the telecover off and plunk the Left-Behind box on top of the bee escape board. No bees fly out when I open the hive because of the bee escape, yet bees in the L-B box can get into the hive directly. This fixes a vexing problem I hade placing the L-B box nose to nose with a hive when I have covered th entrance area with substantial reorientation prompts. And it avoid a problem in the dark.
I always place the hive on the new stand 180 degrees around from whatever direction it faced before, even if that's not the way I want it to face permanently. I'll spin it around over the next few weeks to correct that if needed.
I have experimented with many kinds of re-orientation prompts and this seems the easiest to manage: Get a wooden shipping pallet and lean it up against the front the hive over the entrance area. Weave various leafy branches through the slats of the pallet This way when you want to look at the front entrance, you can just lay the pallet - and all the foliage - down and lift it back up in one go. I slide plastic political signs forward from the both sides of the hive to physically block off a sideways path. Then the bees are forced to negotiate their way through the slats and the branches. This causes them re-orient effectively.
I regularly move my colonies 25 - 500 feet from a winter common stand to farther-apart summer stands, so I do this routinely each spring and fall.
I can go into more detail, if needed. And I have pictures to share.
But I strongly urge you to wait several weeks - there is a lot to be gained, and nothing lost. If you'd like to cheat the hive out somewhat from its current position in the barn to make the final move easier, you can do that a few feet at a time on warmer days beforehand. Unless the bees obliged you by choosing a site right at the entrance.
Nancy