In Texas can an adopted child be excluded from the will?

Anyone anywhere can exclude (or include) anyone they want in a will. Don't confuse that with what the laws are when there is no will, which vary by state.

Generally lawyers advise that each immediate family member be mentioned in a will, even if to leave $1 or to say why nothing is being left, so that lawsuits saying you aren't in your right mind and 'forgot' don't have clout.