Hi Claire! Just to say - try wrapping up and going out when it's vile, just for a short ride. Be prepared for a battle with the wind and to get wet, as long as you know you can get home and get dry straight afterwards. Choose somewhere flattish if you can! I think you will come back exhilarated and a bit proud of yourself, even if you haven't managed to go over 5mph.
I'm saying this from experience - I was out and had only my bike to get back home, with a real storm brewing. When I got back I felt like a real hero, and all toasty and warm too.
Also, I have hardly any cycling-specific clothing, but I do have outdoor stuff including a decent waterproof jacket and nice warm gloves!