It is extremely likely that the race that defeated the Time Lords could travel through time. A war on a single front, space, would almost certainly be easily winnable by the Time Lords. But a war on
two fronts -- space and time -- would be more of a challenge, not to mention never being dealt with before. The Gallifreyans are usually quite secluded, and prefer not to get involved in political issues throughout the galaxy.
Also, yes, the Time Lords are all quite capable of traveling through time, however most of them do not. The Time Lords have "capsules," which are just TARDISes with a less cool name, which they use to travel backwards and forwards in time for research purposes only. As the Doctor says, his people are generally quite boring.
As a matter of fact, that's why he left them in pursuit of adventure in the first place. He was on the run for a while, then they sort of "tolerated" his renegade existence, then I suppose he allied with them loosely, but we all know where they are now.