You mention a lot about how you look like an idiot, or people are wondering what you're doing there, or don't take you seriously. Those are your assumptions. You are letting your insecurities ruin the job for you. I completely understand how that feels, bit the only way to gain confidence at being on site is to do it. Whatever people are thinking is their problem. Don't assume the worst, people rarely think about is as much as we think they do.

No amount of trying to 'blend in' is going to make people not realize that you are small, so stop trying. Own it. Tell your boss that you need to order gear in your size. Tell your coworkers to speak up and if you have to keep reminding them, that's their incompetence, not yours. If you know you need to reach things that are too high, being a step stool. People respect when you are there to get a job done by whatever means necessary.

Pro-tip: whenever I buy new safety gear? The first thing I do is drag it through the dirt to make it look well used.

At some plants the male workers have said creepy things to me when my coworkers are not around

Document and report. If your supervisor isn't handling the situation appropriately, that's what HR is for. You should never feel unsafe in your own company.

And besides all those issues, its freezing cold, the plants are gross and dirty, most sites don't have a decent area to set down your computer and program when you don't need to be walking the floors.

Now we're getting into suck it up territory. Site work is often unglamorous, but everyone there is dealing with the same stuff. Plan ahead and wear appropriate clothing to stay warm. Don't be afraid to get your hands dirty. It's important to not act like you're above what everyone else deals with.

Don't site work is just a part of the type of work that I do, and it means that I have to step out of my comfort zone sometimes. I've also had to learn to accept that some 'blue collar' guys just aren't going to like me or be happy to see me because they just don't think very highly of engineers. Oh well, I'm not paid to get their approval, I'm paid to do my job.

Then again, if there are jobs in your field that don't require those types of site visits and you hate them, than go where you're happiest. You don't have to prove anything to anybody.