In theory a baby monitor would work but you need to be aware of a couple of things:
- A baby monitor would be designed to work indoors at room temperature. Usually these devices have an operating range indicated on them. Put it outside in the cold (I assume 30 degrees is in Fahrenheit?) since you mentioned cold, then you have potential issues with condensation and temperature operating range. Check the operating range and it will almost certainly be around room temperature only and putting it outside in the cold will most likely be below the stated minimum range.
- If you are running it from the mains then you have additional problems with damp/condensation on the wire which could be dangerous. If it's battery powered this is not an issue, but you will then have an issue with battery life as the cold saps the life out of batteries.
I presume you won't have it outside when it's raining, especially if you're running off the mains!!
Since you mentioned inexpensive, are you aware you can stream loads of birdsong on YouTube? It would not be your actual birds you're hearing but depending on your needs it may do the trick.
I hope this gives you a few pointers :)