There are small, easy to handle tow behind sprayers usually sold at places like Tractor Supply. They have a small boom (to spray pastures) and also a wand you can use to spray fencelines or spot treat. There is no PTO; it’s got a small electric pump you can plug into a riding lawnmower or ATV/gator. If that doesn’t work you can mount a small battery on it, charge the battery, and it will work for many hours.
But if you’ve got really problem pastures, spraying them will only provide temporary relief. Mowing will keep weeds down, and spraying will also control them. If you want decent grazing though, you need to start with a soil test. Real weed problems are indicative of soil problems. Many weeds (or undesirable plants in a pasture setting) are indicator species.
A common example is buttercup - indicative of compacted and acidic soils. Henbit proliferates in disturbed or bare soils. You can spray all you want you’re never going to get decent pasture because the soil won’t support it. It also becomes a very expensive and time consuming endeavor; controlling all those weeds.
You can perform the soil test now; the local feed store or extension agent will most likely have the bags you need, and they’ll tell you how to obtain good soil samples. After you get the test results, you’ll know what kind of soil you have and what you need to do to it to grow good nutritious pasture. Then you can work with your extension agent or feed store to fertilize/lime as necessary. Once you get that all squared away, you’ll find your weed problems greatly reduced.