I'm still confused by the question, tho it appears you got answers that work for you.
1. You have a well, 22 feet deep. (How big around is the well pipe, 2 inch, 4 inch, ??)
2. An electric pump froze, so you have no pump/ no water pressure now? (Was this well set up just for your barn, not for the house you still have a well over by the house?)
3. You no longer have electricity to the well area?
Is this what you are saying?
The 'frost free hydrant' is an on/off valve, it is not in any way a water pump. It is exactly what you want if you have pressurized water and a water line buried below frost depth to where you want the hydrant. One very, very important thing with these is that they either need water to be flowing through them, or they need to be open to the air so that the water in the pipe can drain back down. They -cannot- have a hose attached, turned on or off, and let water stand in them. That will freeze them up solid. They must be allowed to drain out when not in use.
If you are trying to pull water out of your 22 foot deep well, you would need a hand well pump with a piston rod and the actual piston pump at the bottom of the pipe. They kinda look like a hydrant, but a much bigger handle and they have a piston pump at the bottom.
Like these, there are other brands:
http://bisonpumps.com
This pump would need to sit directly on top of your well.
There are also solar models available, tho if you have electricity anywhere near a submersible pump would end up an easier choice. I suspect you used an electric pump that was up on the surface, and it froze and busted when it got cold. You should have had a submersible, the whole pump is down at the bottom.
You would not want a 'pitcher hand pump' as they only got about 15 feet and require priming, not suited for you.
So, I think you are asking for a 'hand piston water pump' but if you still have electric there a low power 'submersible electric water pump' would replace what you had without the freezing issues.
Really helps to describe what you have, there are so many types of wells, and so many types of pumps, we all are guessing what you have and where you want to get to...... If you don't know what to call things, go slow and let us help you, but really good to know what it is you have so as to know the best 'bang for the buck' direction to go.....
Paul