Are your rooms small or large? I have a small fan heater that will warm a small (tiny) room in 15 minutes, but doesn't warm a larger one for nearly an hour. It's a 2kw, same as the Dyson, which can warm the larger room in 15 minutes.
You have to be prepared to put up with the noise - the guy said the motor was faster than a F1 car, it's also as noisy! I'm used to it now and I know the way I use it that it's going to save me money on the gas bill. It's not been cold enough for me to use the heating or the fan (apart from the little trial I did to see just how quick it was compared to my little fan) seriously - though I think that may change on the weekend coming up!
I won't put the heating on if it's just me in the house, but I do have a medical condition that means I can't move around much and I feel the cold. I have a few "warmer-uppers" (that are the butt of many jokes in my family) that I use to keep warm. I wear lots of thin layers, topped with a warm, chunky fleece. I wear wool socks and fingerless gloves and a scarf if it's really cold. Going to the loo is an absolute pain, but if I'm warm to go, it's not so bad. I could never wear a onesie - I'd freeze taking stuff up top off for the loo!
I've bought a few things from Lidl that I intend to be buried with - a heated throw, a heated "bat-cape" and a bed warmer. Oh, and remote control sockets (half the price of QVC's last week) so I can put my bed-warmer on an hour before time without hauling myself upstairs. I loved the throw until I tried the shawl thingy. That warms me up a treat in minutes, where the throw would take at least 30. It also seems to warm me up to the core so I don't feel chilled going into different rooms or even hanging washing out. I also have some wheat and gel bags that warm up in the microwave. The gel one goes down my t-shirt when I really feel cold. I'm that cold that they went to bed with me every night through the summer, too.
Cozee Home bedding has been a godsend! No sheet-shock, dries on the line in an hour, NO IRONING (saves a LOT of electricity!).
The Dyson was an extravagance, but I've never been able to warm up in the shower and hate getting out into a chilled room. Now I stay in bed, switch the fan on by remote 15 minutes before getting up and by angling it between my bedroom and bathroom, manage to get warmth in both rooms. My little fan never managed that. On high, you'll also feel a draught rather than warmth unless it's directly in front of you.
If you think about the way you'll use it, I do believe it will save you money on heating bills. And you also need to remember it is noisy on high - I see a lot of reviews comment on this and thought I was prepared for it. I wasn't as it is noisier than I thought. It'll rarely get used as a fan by me, but I also understand that it's just a fan and not an air-conditioning unit (another complaint that crops up in reviews).
and keep one pair as slippers for when it's really cold. I've lined all my shoes and boots with sheepskin since seeing my old GP who suggested it to help chilblains (which I've fortunately only come close to having a few times since). I'm sure it was all the mustard baths I had to try to get warm in a hurry that triggered them. And they never worked properly! Sigh. 
