People who are totally blind cannot perceive light or darkness. Only a "very small" percentage of blind people cannot perceive light.

There are many different degrees of blindness. The definition for blindness in the US and Europe is seeing 20/200 in the better eye when using the best correction possible. Someone seeing 20/200 could certainly tell the difference between night and day. Another definition of legal blindness can be caused by tunnel vision. This too would allow for seeing night and day. Some blindness could leave only "light perception". Again, the blind person in this case would know that the sun is still out. Even in cases where total blindness exists (no light perception), it could still be possible for a person to feel the warmth of the sunlight or hear sounds that are more related to daytime or nighttime. Daytime and nighttime might "feel" different to them as temperature, humidity, sounds, smells, etc change.

If we assume a person is totally blind (i.e., without eyes), it remains possible to identify day or night through skill, training, and experience. Environmental sounds change throughout the day. Some sounds occur more frequently at dawn - anyone who keeps birds as pets is well aware of this. Different animals are active at different times of the day - one can listen for these sounds. Insects provide many audible cues (e.g., cicadas usually sing during the heat of the day). Environmental sounds are also created by human activities. Traffic is heavier during daylight hours than at night. Traffic is heaviest in the morning (e.g., between 07:00 and 09:00) and in the afternoon (e.g., between 16:00 and 18:00). Many similar audible cues exist. A person can roughly identify at what point the sun lies above the horizon, if the day is sufficiently clear. This is done by sensing temperature differences on parts of the body. Warmer areas are facing the sun and cooler ones facing away. There are many other environmental cues that people can use to help identify the time of day. Some people can be trained to keep track of elapsed time fairly accuractely without the use of a clock - their internal clock. This is done partly through experience and partly through changes in their own physiology during the day. No, it is not possible to state the time is precisely 02:23 or 12:10, nor is it always necessary, but one can acquire the skills to estimate the time surprisingly well.

The other answers here are excellent and well written. However, I would like to add this little tidbit: David Berson, professor of neuroscience at Brown University, recently discovered a new class of photoreceptor called intrinsically photosensitive retinal ganglion cells (ipRGCs). These cells, which number about 2,000 per eye, communicate directly with the brain and are responsible for the regulation of circadian rhythms. Berson's study examined the eyes of mice, which are thought to closely approximate the function of human eyes. [http://www.livescience.com/humanbiology/060109_eye_cells.html]

Just to remind yourself, there are blind people around. So all you have to do is ask them, and then you will know it with 100% certainty. If you have trouple finding someone blind walking around the street, you might want to go to a clinic for people who are blind and talk to one of the patients in a waiting area. You might also want to run google search to find some mailing list for CAREGIVERS of people who are blind. Given that their caregivers are able to see, they will be able to participate in the mailing list. So you can ask them to ask their blind patients the question you want to know, and post an answer.

In the US, the legal definition of blindness is 20/200 when corrected with the best possible prescription. A person with 20/200 can make out the second line(from the top)on most eye charts. This same person can see the difference between night and day.