How old are we talking? Its not that it is a big thrill ride but it is fast and kind of jerky. That's what gives it the feeling of being bigger then it is. My 8 year old daughter loved it but she did comment on that it was very "jerky".
My son started riding it when he was 6 and he loved it.
However, it is jerky in that there are lots of twists and turns. It never inverts and there are no super high climbs and drops. I have severe motion sickness, but even I can do one ride on Big Thunder Mountain!
But each and every child is different!
Have they ever done Goofy's Barnstormer? You might use this as a "stepping stone." That is, try The Great Goofini coaster in Storybook Circus and if that goes well, try Big Thunder.
I would let the children watch people ride for a bit, and let them decide. Definitely do NOT push it on them, because that is one memory you do not want to make! There is a great viewing spot for Big Thunder Mountain past the entrance and up a little hill. It used to be a Kodak Picture Spot. That would be a great place to let them watch the coasters come around and see if they would like to ride.
Most drops are with turns. This was next step up from barnstormer. My wife, who hates rollercoasters, likes this ride. I mean HATES!!!!!

Problem is from my research this is a very popular ride. The day we do Aventure land and Frontier land we will be getting to the park at 11:10 for our sons Pirates League appointments. Chances are we wil be getting to Big Thunder Mountain some time Between 1:00 and 3:00 so I thought it may be best if we were goint to do it as a FP+ option. May be too late to scdeule some other FP+ option if they decide against it.
5,7,and will turn 9 year old at the end of this month.
uhm that sounds promising. May have to add this one to the list. Is there alot of fun things to look at on this ride? One thing about Disney rides I find unbeatable is the themes and detail of the rides.

Here it is, so you can judge for yourself. It obviously feels a little different when you are actually on it.
http://youtu.be/ZmmteiM_K1Q