There are hadith indicating that the prophet Muhammad and the Arab armies broke fast during military campaigns.
It's worth noting as well that fasting is hardly unique to Muslims. The traditional Christian calendar had a huge number of fast days and feast days.
Likewise the Arab armies were not uniformly Muslim.
For the hadith in question see the following: http://sunnah.com/tirmidhi/8/33
http://sunnah.com/bukhari/64/309
http://sunnah.com/bukhari/56/44 (NB: Jihad here is used to translate "al-Ghazw", a military raid)
Edit: this is obviously significantly after the time period in question, but the effects of hydration on combat in hot environments wasn't really understood until the 20th century. The Israelis were some of the first to develop tactical doctrine on this and it reputedly gave them a significant advantage in the '67 war. The following abstract refers to it, unfortunately I can't get the PDF to download: http://oai.dtic.mil/oai/oai?verb=getRecord&metadataPrefix=html&identifier=ADA113477
You can stop fasting if you are a traveler or are facing other hardship. Presumably this includes soldiers because like you thought it would be impractical to fast and fight.