I use Logic Pro X on an EEEPC 1201n, 4GB of RAM, but I really don't know how the Atom 330 CPU compares to the D250. I can open up to 8 tracks, one being the Drummer A.I. track, before getting the dreaded system overload box and having to resort to freeze tracks and all that jazz. Heavy plug-ins like Native Instruments will let me use even fewer tracks. One interesting thing I noticed is that there's a graphics-related (yes, graphics) bottleneck, and to make the musical typing to work without lags, I must never zoom the track horizontally. I suppose this would be even worse with your netbook, since its graphics aren't supported at all. That's it. Hope my experiences be of some help.
All the best!
P.S.: I forgot to mention that my 1201n is OC'd to 2 GHz.
P.P.S.: also, if I'm not wrong, the Aspire One D250 uses an Atom N270, of which the integrated graphics are supported by OSX up to Lion, but unfortunately is a 32-bit only CPU, meaning no Mountain Lion/Mavericks, thus no Logic Pro X.
P.P.P.S.: buy a second-handed MacBook White Unibody, making sure it's a later model with 64-bit EFI: those can run Mavericks, and you can find them on Ebay at a fairly reasonable price.