I think Rock is right, it looks like generic roadside Southwestern Pueblo Pottery. Very common souvenirs when people would take roadtrip vacations to see the Grand Canyon/Vegas/California. Some examples are worth a ton of money, but most are just nice display pieces. I don't really see much chance that it was found on the farm, it doesn't look like it's spent any significant time buried in the ground or in a cave.
Google Pueblo Pottery and you'll find a lot of pictures/webpages, you might find something that matches the style (color, shape, brush strokes, etc.)
Look on the bottom for spin marks (from a wheel) or perhaps the remnants of a signature. Wheel marks would indicate it was a mass produced decorative piece, furniture stores and mall stores sold them from Mexico and China. A signature might indicate it's worth some money.
