There's two different kinds of droning I get from my car (and when my lady friend isn't in it!). These are:
When braking (you specifically mentioned slowing down), sounds a little bit like coming out of warp speed according to one of my passengers. It only started since I had the front discs and pads replaced, and it's because they haven't yet bedded in properly - it went away again within about a month (I don't drive a lot).
The other is on certain roads, and at certain speeds (particularly the odd yellow tarmac on some parts of the M25), I get a drone coming through the entire cabin, but it's only at particular speeds so I assume it's just a resonant frequency.
If you think it might be the tyres are worn then go and have a look - make sure that you turn the front wheels right the way to one side so that you can check the inside edges as well at the front. Also check that the tyre pressure is correct.