You've got to raise your mileage for starters. Increase your 'base mileage' until riding 3 km becomes easy. Improve your cardio fitness whether by 'race walking', swimming, running, aerobics, etc. Committing to fitness as a lifestyle takes a mental approach more than anything else. I swim and weight train while maintaining a fairly high mileage base. In other words you need to get in better shape.
There are many jackets that will do the job you're requiring. Personally, I use a Pearl Izumi Barrier jacket that's cycling specific. It has elongated arms and back panel w/vents to allow better evaporation. It's made of 'wind resistant' material. I got mine on an 'old stock' discount for 70% off list price. You'll still need some sort of base layer...silk is VERY good and relatively inexpensive. Also, a balaclava under one's helmet works wonders for heat retention. Not to mention a helmet cover. Nashbar makes a good one and it doesn't cost much. There've been many threads where people list what they wear according to temp, weather conditions, etc. Do a general search and go to the 'Winter Cycling' and 'Touring' sub forums. There is a ton of info there, also.