I don't really understand the difference but I know a song where they say : 朝目が覚める（あさめがさめる）so I think it's sounds more natural but not sure... -the song is here :
In general, deictic time expressions (whose meaning depends on context) like 昨日 or 来年 do not use に, while absolute ones like 七時 or 二月 do. Certain expressions, like 朝 or 冬, can be used either way. In which case, に emphasizes the point in time.
For example, compare the following sentences:
常に、朝喫茶店へ行く = I always go to the cafe in the morning
殺人の朝に喫茶店へ行った = I went to the cafe on the morning of the murder
To add to what gdartfow is saying, this discussion of absolute/relative time phrases is also mentioned in the Basic Particles lesson under Resources > Japanese Basics (in renshuu's menu).
A quick and pretty effective way is to know what is and isn't absolute is this:
If you can point to it on a calendar or a clock, it's absolute, and gets the に added to it.
