I used to take all my oil painting supplies with me when I traveled, easel, chair, paints, brushes, etc. It is nice to have all your supplies with you. However, it costs a lot to carry an extra suitcase for all of this. I have taken all that stuff to Europe four times and many times to Cape Cod. I have a rolling backpack that will hold of these supplies, though you can't take oil paint or mediums (like turpentine) through security. Those have to go in your luggage. I bury them under my clothes, just in case.
These days, I have cut back extensively on the supplies I carry. I take a sketch book, small set of watercolors, brushes, pencil, ink marker and camera. On site, I do a pencil sketch, then apply ink and then watercolor. I finish by taking photos of the site to help me create an oil painting in my studio. Then I also have nice watercolor journals of my trips.