Tower Controller described a go-around event when misjudging the time required for an aircraft to take off from the ILS critical hold line position; the Reporter acknowledges a need for increased vigilance during these types of weather conditions.

Narrative

I was working Local Control and had a Citation waiting to depart XXL; there was a regional jet landing and Aircraft Y was about 5 miles in trail. After the first jet landed; I put the Citation in position and told him to be ready to go because it was IFR conditions and I needed 2 miles increasing to 3. As the first jet cleared the runway; I cleared the Citation for take off but since he was holding short of the critical area; he was just then pulling onto the runway. Aircraft Y was on about a 2 mile final at that point and I realized it wasn't going to work and I cancelled the Citations take off clearance and instructed him to exit the runway to the right. He must not have heard me because I got no response and he continued to take off. I sent Aircraft Y around on about a little over a mile final and turned him 90 degrees to the left. I turned the Citation 20 degrees to the right although by that time Aircraft Y was diverging. From now on; working in those conditions I need to slow things down and not try to hit the small gaps. I also need to keep my awareness up; I got focused on the first arrival clearing the runway instead of watching the Citation get into position.