Goats are allergic to water that is not currently inhabiting a special water trough, so they won't get into your pond.
The standard rule of thumb for goats, if you want them to get a significant portion of their nutrition from browse, is:
Standard size-- 5 goats per acre.
Mini size-- 8 goats per acre
Nigerian Dwarf size-- 10 goats per acre.
If you are providing ALL nutritional needs and do not expect the goats to have to forage for ANY of their food, then you need about
:
Standard size-- 100 sq. ft per goat. (10' x 10')
Mini-- 65 sq. ft per goat (about an 8' x 8')
Nigerian Dwarf-- 36 sq. ft. per goat (about 6' x 6')
So, if you are providing nearly all of their nutritional needs, then your 50' x 70' area with pond will be FINE.

They will also clear out any underbrush you might have back there.