I have not found records of night warfare in the Hittite period in question. However, I have found evidence of night warfare from the period of Classical Antiquity, and earlier. For example Yehoshua sends 30000 men to lie in ambush at Ai, as recorded in Joshua (8:4), although that was just troop movement, but not battle. More significantly, in I Maccabees (4:1-5) Gorgias attempts to attack Judas Maccabeus at night. Similarly, II Macabees (8:7) states that Judas Maccabeus preferred surprising enemies at night. Additionally, the Battle of Thermopylae was fought at night as recorded by Diodorus, although Herodotus doesn't mention this, and many historians are skeptical (see here).
So, it seems that fighting at night was not so unheard of as to be a miracle. Notably, I Samuel (14:36) portrays Shaul planning on attacking the Philistines at night, although he does not go through with this battle. Context (such as the troops willingness) indicates that this was not completely out of the ordinary or miraculous.
Additionally, Judges (7:9-22) portrays Gideon conducting a night battle against the Midianites. Eric Cline writes here that this is the first night battle in history for which we have a detailed account. I do not see any indication from there whether this was standard. Notably, Gideon is scared and commanded to proceed by God, but I see no indication that this was because it was night.
According to this book, night warfare had always been practiced, but was considered risky, difficult, and exceptional.
Perhaps we see Avraham's willingness to risk himself to save Lot. On the other hand, it seems that this was a pursuit that dragged into night (see Rashi and Ramban to 14:15). It could be argued that Avraham was less exceptional since battles continuing into the night were more common than those starting at night (see here). However, that seems to have been due to the difficulty of coordinating and disengaging armies, while Avraham and his relatively small party (just 318) could have likely disengaged, and called off the pursuit. Thus, it seems likely that this battle was somewhat exceptional, which is likely why the verse mentions the nighttime in the first place.
Notably, and this doesn't contradict the suggestion that he bravely risked himself through the night pursuit, Seforno (ibid) suggests that he used the cover of night to hide the small size of his party.
It should be noted, that R. Yosef Kara (viewable here) reads the verse differently, understanding that Avraham sped up the chase to avoid it extending into the night given the impracticality of night warfare.