First off, do your date filename the other way round:
2012-04-01.txt
That way, they are automatically sorted by date rather than all the first of the month, all the second of the month, as so on - getting to the newest and oldest becomes extremely simple.
It's pretty simple, you don't even need to check if the file exists:
List<string> lines = new List<string>();
lines.Add("user 1, " + DateTime.Now);
lines.Add("user 2, " + DateTime.Now);
File.AppendAllLines(@"D:\Temp\" + DateTime.Now.ToString("yyyy-MM-dd") + ".txt", lines);
The various File.AppendXXX methods create the file if it doesn't exist, and add the data if it does.