My horse uses a 52" girth (with elastic on both sides). Its a tad bit big but I'm not sure if a 50" girth (also with elastic on both sides) would fit. What should I do?

I've just gone from a 46" girth to a 42" and it fits my mare just fine, so I highly doubt 2 inches off a 52" girth will really make that much of a difference. If it's a bit big then I'm sure it will fit, especially if it's elasticated.
Borrow a 50” and try it.
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