From: Albuquerque, NM
It should be pointed out that the number you see on the stack is not the unit's size, but rather its combat effectiveness or PWR. PWR is influenced by a number of factors but, most importantly, by the experience and quality of both leadership and troops. The South starts with a number of top notch commanders, while the top level commanders for the North are largely incompetent.
While using FOW the enemy unit information is hidden from you. You can possibly get a peek into the enemy by employing your cavalry. This may or may not work depending upon the cavalry available to the enemy, but if it does you'll know if you're facing a brigade, a division, a full Corps, or all of the above.
I have played several GC as both USA and CSA and in my last USA GC, Grant and Sherman were able to clear Western Tennesse and make an early Vicksburg campaign possible by mid-1862. The ability to create a powerful Union force is there if the player takes advantage of the choices available to them. There are excellent Union commanders waiting on the wings in subordinate postions and you as the player need to cultivate and raise them up.
As for Militia, they are very low quality troops and should never be deliberatedly placed into a combat unit. If I have to recruit them, I will first attach them to an HQ with some training capability (i.e. a HQ support unit) to get them up to at least an infantry level. Fortunately, the Union has enough resources to be able to recruit line infantry and elite infantry without having to rely upon milita.