Me and both of my sisters grew up with severe asthma and traveled a fair amount with a full arsenal of medication and a nebulizer. This was back in the mid to late 90's so things have changed some since then, but even back then the mini nebulizer really saved us on a few trips! We found that inhalers and our other medications were easy to use on the go, but after being active and energetic thanks to being away from home and in a fun setting it was easier for us to have attacks at night. Particularly after swimming (when we went back to a chilly hotel room). I don't think we would have been able to travel back when I was younger if we hadn't of had our travel size nebulizer to go along with us. It can be a drag to sit and have to do a breathing treatment when you're away from home and wanting to do fun things, but it's definitely not a huge inconvenience.
The only thing I would warn about buying them now is to avoid using places like ebay and maybe even Amazon. I bought a new mini nebulizer for myself a few months ago to bring on my upcoming trip and the thing won't fit my standard sized tubing or masks I've had forever. It didn't come with any either, and customer service still hasn't gotten back to me on ordering the right parts, so I'd just say be cautious if you're not ordering from an actual medical supply place.
I have severe asthma, travel with a MicroAir by Omron. I have tried several other brands, but it is by far my favorite. I just managed to get a fabulous price of $160 on one. I don't use a wall plug in one at all (unless on publicist), just the MicroAir. It is discreet enough I use it on planes, trains, & even WDW!