Does the size of a school (e.g. Texas A&M with more than 40k students) matter at all, especially concerning the courses? I mean, do big universities tend to have courses which are filled up and hence have to be taken in winter/summer semester? (Stony Brook, for example, has 24k students and there is no chance to get into a lab in the regular semester)
Size certainly matters concerning being able to enroll in courses. Enrolling a larger undergraduate population vs. a smaller one in classes undoubtedly means having a harder time getting into the courses you want without priority by seniority. That doesn't mean you run the chance of never getting the courses you need; rather, you might not get them when you want them and end up, like you said, taking them over a winter/summer break. (That's speaking from my experience at UCLA, with our 26k undergrads.)
I don't know very much about Texas A&M in particular, but I do know that they're known for the math and sciences mostly. Therefore, a large portion of the students there are going to be after the chemistry labs you're probably going after. That, plus a large undergrad enrollment, seems to imply you'd have issues with enrollment in the courses you want, but like I said, it doesn't mean you'll never be able to take your labs.
If getting the courses you want, when you want them is your primary concern, I would advise looking into some smaller schools. But even that's no guarantee!