Well that clarifies it- very late winter/ early Spring is generally the best time to collect most deciduous species including Hornbeam. And, yes, with most doing it prior to bud break is ideal. I wouldn't say they MUST be collected then, but that is definitely the sweet spot. The Fakl can be a good time as well in MY area at least where we generally do not have brutal winters and the worst of the cold tends to hit late like January/ early Feb... I do not know your climate very well to be able to advise on the difference between January and Feb where you live, but everything I hear about the long term forecasts for our region says Jan- March may see record breaking cold and precipitation! If that is the case... And it is the nasty freezing mess people are projecting, I would not recommend pulling a tree out of the ground in January... I'd wait until late Feb. on the other hand, if we stay at 79 degrees... Maybe you could dig them now and they'd be fine. The "norm" has kind of gone out the window so far this "Winter". I have bulbs that bloom in March/ April popping in my garden right NOW! A Korean Hornbeam I bought in October has tried to grow new buds ever since I got it home... Junipers are still growing like it is Spring time and I am not sure if any of my Maples- except the Tridents- are even fully dormant yet. So, who knows what is coming!?!.
In a normal year though, normal conditions.... February is probably what I would recommend.
Notable exceptions- Water Elm and Bald Cypress seem to do best when collected in mid-summer around here according my my experience and what I have been told by others who have done a lot more collecting than me. Beyond that, go for Early Spri/ late Winter...
The best advice I can give you is: AFTER CARE IS MORE IMPORTANT THAN TIMING! You can miss by a couple weeks one way or another, or even collect something in a pinch at what most people tell you is the absolute WRONG TIME and still have success if you do a good job caring for the tree. You can also have total failure even if you collect at the perfect time if your after care sucks.