I was in Tallin in late June, but still there was heavy rain for a whole day. Of course it's not a real danger, more of a warning actually. You miss out on the beautiful colours of Tallin, but at least you don't have the supersonic guided tours from the cruise ships!
It's not so much the rain, although there is that; it's what happens to the rain after it falls that you need the waterproofs for. I was advised to bring a good pair of boots with me before I came, but I think you'll need a good coat too... and a hat... maybe an umbrella too.
The problem is that it rains in winter. A lot. And that rain has to go somewhere. Where it goes in Tallinn is into the many cracks in the uneven roads and pavement, and into the gutters that channel the icy water from the roofs of the city... straight down the back of your neck.
It's a real challenge sometimes to skip over the puddles, avoid splashing your fellow pedestrians, and prevent the chill trickle down your spine. I even contemplated making a game out of it: The Tallinn Water Dodge. I'm sure Estonians would be brilliant at it.
It gets worse. After the water falls, forms puddles, and splashes down your back: It freezes. You will need good balance, as well as a good grip, to avoid slipping when that water turns the uneven roads and cobbled streets, into a flat, smooth icing rink.
Don't complain - what did you expect? You're as far north as Alaska and the Orkney Islands in Tallinn!