Thank you for your question. The Shulchan Aruch (Yoreh De'ah 116,1) writes that drinks that were left uncovered are forbidden to drink, because perhaps a snake drank from it and left some of it's poison in it. This applies not only to wine, but also water and milk (and some sources include other drinks also). The source for this law is found in the Mishna (Trumot 8,4).
Based on this the wine would be forbidden if it was left unattended and uncovered even for a very short time, whether during the night or day. However the Shulchan Aruch goes on to say that nowadays that snakes are not common in our houses this prohibition does not apply. So, unless you left your wine uncovered in a place where there are snakes (or you happen to have a pet rattle-snake) it is permitted to drink it.
There are those who even though they live in locations were there are no snakes refrain from drinking drinks that were left uncovered. The Vilna Gaon for example believed that it is dangerous for spiritual reasons to drink things left uncovered. Others are strict because they argue that once the Rabbis enacted an edict to forbid uncovered dinks we are not able to rescind the edict, even when it does not seem to apply. If one follows these stricter opinions it is important to know that there are various definitions of exactly what is considered "uncovered" and how long and in what situations it becomes forbidden (for example drinks left in a fridge are not forbidden).
But the basic halacha is as the Shulchan Aruch rules – uncovered drinks are permitted.
There is a question about using such wine for Kiddush. The Shulchan Aruch (Orech Haim, 272,1) writes that wine that had been left uncovered should not be used for Kiddush. The reason is that Kiddush wine should be of a fine quality for the honor of the mitzvah, and so wine left uncovered, which lowers it quality, should, preferably not be used. There is some discussion about the length of time being left uncovered is problematic in this issue – some people learning from seder night when we pour the second cup a long time before drinking it, and others rejecting that proof (see Shmirat Shabbat KeHilchatah 47,18 and the footnotes). None the less, if it was left out uncovered all night, as in your case, you should not use it for Kiddush (see the Aruch HaShulchan 272,5).
In summary – wine left uncovered overnight should not be used for Kiddush, but, according to the basic halacha, it may be drunk. There are those who are strict and refrain from drinking wine that was left uncovered and unsupervised, and they have halachic opinions upon whom to rely.