It is hard to say without more information.
If all you want to do is fill up a water trough.... and not really concerned how long it takes, 1" will do fine.
To determine [estimate] how much water flow will you get from a 1" line depends on several things. Will you be connecting the new line from the line that feeds your house or connecting somewhere in the house?
What size existing water lines do you have? How much water pressure do you typically have at your house?
If you will have 1" line from the main line all the way to the barn.... you can expect to get about 5 to 8 gpm flow at the barn. If you connect to the back of your house where the line size is 3/4" or smaller this will restrict the flow. Max flow might be 2 to 4 gpm.
Also the type line you run would effect these numbers a little. Will you be using steel pipe [galvanize], PVC or black tubing? In some cases, steel pipe in not good to the very high corrosion rates.
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