Yes you can order either the Mini 10 or the Mini 10v with Ubuntu. You could later install XP if you wish; there's nothing "inside" that would prevent XP from running on one that came with Ubuntu. You can get all the XP drivers you need from Dell's website.
A word of caution on Ubuntu and the Mini 10 (1010). There are issues with Linux drivers for the GMA 500 graphics processor on the Poulsbo chipset (long story, you can Google if you are interested). Dell offers Ubuntu 8.04 on the Mini 10 so maybe they have worked out the driver problem themselves. However, there are real issues if you want to try the newest Ubuntu 9.04. I have been able to install it on the Mini 10 (both 9.04 desktop and 9.04 Netbook Remix) but it doesn't work good at all. Really bad.
The Mini 10v should run Ubuntu quite well because of the N270 processor.
FWIW, Depending on which Mini 10 you are looking at, Ubuntu or XP on the Mini 10v are the same price at this point. If there isn't a price premium for XP, you might consider buying it with XP; you can always download the Dell/Ubuntu image and install that later.