Contact solution (or saline solution) will freeze just below the freezing point of water. So you should expect contact solution to freeze when temperatures drop just below the freezing point or to around 30 °F (−1 °C).
To put this in perspective, sea water is a saline solution and at typical salinity, sea water freezes at about 28 °Fahrenheit (−2 °C). The freezing point of seawater will be lower as salt concentration increases. Contact solution has less salt concentration than sea water, thus contact solution should freeze before sea water.
On average, seawater in the world's oceans has a salinity of about 3.5% (35 g/L). This means that every kilogram of seawater has approximately 35 grams of dissolved salts.
On average, contact solution (saline solution) has a salinity of 0.9% (9 g/L) This means that every kilogram of contact solution has approximately 9 grams of dissolved salts.
Keep in mind, if you want to be on the safe side, in general if the temperature is at or below the freezing point, you should keep your contact solution and any contacts stored in a contact case warm, by keeping them close to your body or in a sleeping bag at night while winter camping.