TPM or not TPM, that is the winter-time question

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My car has the tire pressure monitoring feature. For the winter I want to put steel wheels and aggressive snows (rear-drive vehicle) on the car. But steel wheels do not accomodate the monitors. Must I use the TPM? Trying to avoid the added expense of alloys plus the TPM.

I want to put steel wheels and aggressive snows

No you don’t. You want steel wheels and WINTER tyres. They are a different technology than snow tyres and work much bette.

You could ignore the error light and make sure you check the tyres often. (Note: sorry if I have missed something like a buzzer that might come on rather than just the light.

How about you just have some winter tires mounted on your normal wheels and just switch them out with the seasons?

You do not have to use the TPMS. You can ignore the light. Just check your pressure regularly. It will not affect any ther system or render useless and warnings.