I don’t know about cross-stitching, but you could do a big logo with intarsia (link to video).
Find a graphic online somewhere with the logo you want. Download it and load into a photo-editing program (photoshop, paint shop pro, paint.net, etc.) Superimpose a grid on top of it, and make sure all of the boxes are filled with either the main color or the contrasting color. Voila, you have a colorwork chart. Knit!
(I use paint.net for charting. It’s free, it’s easy, and there’s a free plug-in that automatically generates grids for you!)
By the way, since intarsia is knit in stockinette, which rolls, you should put a garter/seed stitch/ribbing border along the edges to prevent rolling, if you want it to lie flat.
(Or, alternatively, you could apply the same technique with double knitting (link to video) which will lie flat and give you a reverse of the image on the other side.)