Doing an internship and the short answer questions say no more than 200 words, is 250 permissible?
Given that 250 is more than 200 and they explicitly say “no more than 200,” I would cut your response down. 50 words shouldn’t be super hard – something can always be said more concisely.
Will the college really take points off for that though? As long as it is of reasonable length would they just ignore the word count?
Stick to 200 words, and stick hard. Some online forms will truncate what you write without telling you. Sometimes the form will give you a warning, like when you try to type too many characters in a Tweet. Other forms will appear to accept what you’ve written, but will only display the first 200 words when the recipient looks at it.
Also, this is an internship application, right? So it’s like a job application. Going over the limit is pretty much advertising that you don’t follow instructions, especially if, in your own opinion, you think the departure is “reasonable.” 
They can treat it as strictly or as leniently as they want, so who knows. But I would say it doesn’t look good if an applicant chooses to ignore straightforward directions.
If you’re entering the responses in an online form it may also cut off automatically after 200 words, which would ruin the message you’re trying to convey more than selectively paring it down.