So, Syrian rue seeds were left in a mailbox for about four to five days. It gets freezing cold at night and warms back up during the day (above freezing). This happened for four days.

Do the seeds lose effectiveness if left out in freezing temperatures like that or left outside like that? I tried searching around, but never seen anyone ask.

Just curious is all.

The harmala alkaloids in the rue seeds are not harmed in any way by freezing. To the contrary, cold temperature are a means of preserving chemical substances. The harmala alkaloids are very stable and wouldn't need to be frozen even, but it will not hurt.

The syrian rue plant is a desert plant, deserts can be very cold at times and even freeze. I would not be surprized if even the living plant itself can endure frosts. Very likely, you can still plant and germinate the seeds if you want to.

For some plants, this process may even aid germination! Stratification.