Most people wouldn't be able to tell you the difference between a road bike and cyclocross bike... they are very very similar.
Most cyclocross bikes are designed around road bike but with the following differneces:
1) Slightly higher bottom bracket clearance. How far is the bottom of the bike where the pedals as from the ground. Slightly different geometry will give you better clearance over logs.
2) Slightly studier (and therefore heavier) frames. You want it to be tough over all the off road bumps.
3) Top pull or disc brakes instead of caliper brakes to aid in installation of larger tires. Since you'll want more tread on your tires, you'll want brakes that fit around the bigger tires.
4) Secondary "top bar" brake levers on the top of your handle bars in addition to the integrated brakes on your hoods. This is because you may be doing more top bar riding and you don't want to have to change hand positions to brake.
5) Different shifters - Some people promote bar end shifters instead of integrated brake/shifters. I've heard its a reliability thing if your getting really muddy. I just recently saw a cyclocross bike with a some new style integrated shifters.
As far as all of these features go... I think that a cyclocross bike or a sturdy "commuter" bike would be great for what you're looking for. I think that tire tread is over rated as a speed/comfort thing... I choose my tires based on the weather... in the winter I want more tread and a tougher tire... in the summer I don't mind using "racing tires"... but really even at 20-25mphs I know that tire tread has very little to do with my performance.