Crossing a road
You may cross straight over a public road if you stop, yield to traffic, and cross perpendicular (straight across, not along it), with your headlights and taillights on. On a divided highway, cross only at an intersection.
Off-roading / Riding on roads
Short version: usually no. Here's the default rule, the handful of narrow exceptions, and why "street legal in another state" doesn't help you in Texas.
You may use an OHV on a road only in these specific situations. Master-planned communities with the right approvals, and government, utility, and public-safety vehicles, have their own allowances.
You may cross straight over a public road if you stop, yield to traffic, and cross perpendicular (straight across, not along it), with your headlights and taillights on. On a divided highway, cross only at an intersection.
For agricultural or utility work you may drive an OHV on a road (not an interstate or limited-access highway), in the daytime, up to 25 miles from home base, with the lights on and a triangular orange flag flown at least 6 feet above the ground. For this use, the helmet, eye-protection, and safety-certificate rules don't apply, and no license plate is required.
A machine with an Off-Highway Vehicle license plate may use a road posted 35 mph or less, in the daytime, within 2 miles of where it's parked, to get to and from a golf course - and to cross intersections.
Cities and certain counties can approve specific roads (35 mph or less) for OHV use. On those roads your machine must display the OHV license plate, and if you're going 25 mph or less you also need a slow-moving-vehicle emblem (the orange triangle).
Visitors
Texas does not honor other states' OHV registrations or decals. If you're visiting to ride public land, buy the Texas OHV decal. And a side-by-side that's 'street legal' in another state still has to follow Texas road rules here.
Official sources
Road-use rules come from Transportation Code Ch. 551A and TxDMV; which specific roads are approved is a local decision.
Caution: The road-use rules have been amended in recent years, and road approval is local. Check the statute and your city or county before riding on any road.