Just because there is an available trash can, doesn't mean it's open for public use. In the state of Texas, dumping trash into another's trash can, dumpster, property, drainage ditches, alleyways or etc., can result in hefty fees and fines or even jail time. There's definitely no messing with Texas!
Another side note is a person cannot dump their own trash on their own property as it's known as Litter Abatement and has a penalty ranging from a misdemeanor to state jail at a felony level. The penalty is based off of weight or the volume of the waste.
To report illegal dumping or littering, visit TxDot's Report a Litterer at https://www.dontmesswithtexas.org/get-involved/report-a-litterer/. TxDot and the DMV will work together to locate the litterer and send them a letter as a reminder to keep trash off the roads or a fine depending how many times the litterer has been reported.
Messing with Texas is something that is not tolerable and not worth the fine. When trash starts to build up, give Bin There Dump That a call or find your closest public trash can to throw waste away.