The different axial speeds of the mouse in Ultima 8 are the result of the game specifically instructing the mouse driver to handle pointer motion that way. I thought at first it might be a DOSBox issue of some kind, but the code in the game is very straightforward about how it programs the mickey-to-pixel ratios of the mouse driver.
I think the faster horizontal speed serves a purpose. To make The Avatar run, the mouse pointer must be moved almost to the edges of the screen. If the mouse movement speed is the same on both axes, you have to physically move your mouse further to run horizontally than vertically because of the rectangular screen resolution. The faster horizontal speed is probably the game designers' attempt to have the mouse move in a square area while the mouse pointer moves in a rectangular area. It sort of works for moving around, but when you use the mouse to click on items, dialogue choices, and interface elements, the different axial speeds can be difficult to get used to.
If you find the different speeds more annoying then useful, the TSR is an easy way to force the game to use equal speeds on both axes. To use the TSR program, just run it before running the game. It's intended for Ultima 8 only, and probably won't have an effect on other games.