It seems to me that the boots I'm imagining them to have are very smooth on the bottom. How the hell would they charge at the enemy in dewy or wet grass, or in the middle of rainfall? How would they quickly change directions in the melee? It keeps me up at night.
That is an incredibly general question. What period and what military are you asking about?
I can give you some information about the Australian Army, which used a standard boot. That is, everyone was issued with the line infantry boot.
Approximately during the Vietnam War, the previous “AB Boot” was replaced by the “GP Boot”. The GP Boot was a high black leather boot extending to mid-calf, lace up, with the sides of the tongue sewn to the boot to make it as watertight as possible (not very successfully) and a rubber sole with a raised pattern to provide traction. The boot issued for use in Vietnam included a light steel plate in the sole as a protection against sharp stakes etc. The boot provided good ankle support, good traction, protection against penetration but took a long time to dry out if it got really wet. It needed to be removed and aired to dry. The Australian Army has made various changes since to improve comfort and wear, including a fully moulded sole, but the general shape of the current issue boot is similar.
Prior to the GP Boot, the AB Boot was a black leather lace up boot, with a separate heavy leather toe cap, reaching to the top of the ankle. Protection for the calf was provided by either cloth puttees or canvas gaiters. In the later issues of the boot the soles were rubber as for the GP Boot but in earlier versions (i.e. for most of the life of the type) the soles and heels were leather with hobnails and horseshoe. That is, a pattern of nails with high heads, like flat topped pyramids, were driven into the soles with the heads protruding to provide traction and a U-shaped piece of iron was countersunk around the back of the heel. The boot provided good protection for the foot, not much support for the ankle, reasonable traction on surfaces where the hobnails could dig in (very slippery on wet rock) and tended to mark wooden surfaces like polished floors.
I’m not sure of your issue with rainfall. In deep mud the issue isn’t traction, it is whether the boot stays attached to the foot when you drag it up. Both these types had a long lace up keeping them tightly attached. It was time consuming to put them on or off.