Travelling to Tallinn in 3 weeks, some advice needed for a first timer

Hello!

I've booked a short trip to Tallinn for around the end of the month, as an anniversary present to my SO.

We're going to the shooting range for a couple of hours on the 2nd day of our trip partly for work reasons and partly for fun.

What else can we do whilst we're in town?

I understand it's going to be extremely cold. We have warm coats and snow shoes/thermals... are these overkill?

What do you recommend we do/wear? Any help would be great.

I'm a strict vegetarian, any advice on restaurants?

Thanks.