The simple arrangement would need you to work out where you could mount the magnet and reed switch so they they are next to each other when the sign is in place - and when the sign is moved, the magnet is taken away from the reed switch.
In this setup, the reed switch is closed when the sign is where it is meant to be and open when the sign is moved. This is exactly the scenario you described - and by using the packaged alarm system reed switch and magnet, it provides you with an (almost) outdoor ready solution. This arrangement should be able to stand up to quite cold situations and by taking care of any gaps (in the cases) and protecting the electrical connections, it has the ability to be quite weatherproof. The only caution I would offer is to keep an eye on the potential for mechanical damage - and, perhaps, UV affecting the cases.
There is an alternate approach.
By placing a second magnet (called a bias magnet) next to the reed switch, so that it's magnetic poles are the opposite of the first, the two magnetic fields cancel out and the reed switch will remain open when the sign is in place. Then, when the sign is taken and the first magnet moves away, the second (bias) magnet will cause the reed switch to close. This gives you a circuit that is normally open, but will close when your sign is moved.
Edit: Just a word of warning - you might have to do a little experimentation to get the bias magnet is the right position for the best operation.
There is also a third option.
You can get reed switches that have three connections. A common terminal, one that is normally open and another that is normally closed. It can act as a single pole changeover switch - or you just use the common and one terminal for NO or the other for NC operation:
What it looks like inside:

| . . | The pre-packaged alarm system version:

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Edit: Minor changes for clarification.