Yes, but not for an extended period of time. Try to get it up to at least 70 asap. Why is the temp so low? My platty tank got down to 65 when I moved and it took about 3 hours to get it back up in the 70's. No problems.
I would try to keep it at least at 70 as was mentioned. Mine are doing great at 76F. They aren't cold water fish and the common tank doesn't have the resources that a wild river or lake does in finding warm hiding spots at night and in the winter.
If you are looking for a small coldwater fish then think about the White Cloud Mountain Minnow. 65F is great for them.