Hats

It goes without saying that you'd need a proper hat, and there are some models that can protect your face as well as your frontal lobes. Here are some less common options that can provide superior protection to your gentle facial features.

Beard hats

Yes, I know -- they look hilarious. From second-hand experience, they work wonders (a friend of mine that lives only 300 km south of the Polar circle has one, and he swears by it). This will keep almost your whole face warm, and will be especially helpful in windy weather.

Ba(la)clava

For that extra special spec-ops look. Combine with wired headset and stern look for extra confusion. I wouldn't wear one in civilized company even if my life depends on it, but don't count it against me.

^{Disclaimer: The author will not be held liable if you get arrested for suspicious behaviour when following this advice.}

Other means of protection

Yet more ideas that couldn't be placed in other categories.

Grow a beard

Might not be an option for you particularly, but in Scandinavia beards and all sorts of facial hair are common, and not only as a fashion statement. This works essentially as a non-detachable beard hat, with increased social acceptance.

The Scarf

If you already happen to have a scarf, then you could wrap it up to cover your chin and possibly your nose. Slightly better appearance as far as aesthetics go (definitely less curious looks than those fancy beard hat thingies), but you'll need to do this right the first time, as any major adjustments when you are out in the cold are simply not possible, or at least -- not preferable.

^{This was part of a bigger answer originally, but was split in two for better cohesion.}

As the others have already said, this jacket will not be enough. The temperature ranges you cite do not reflect the fact that temperatures routinely go below zero at night, and in presence of strong winds and high humidity (especially in coastal regions), the FeelsLike^® temperatures would be 5-10 degrees lower. For this reason, I'd look for a wind-proof jacket, even if it is not as thick -- it will certainly be lighter and easier to pack. It's ideal for snow-less environment, and will serve you well even if temperatures fall slightly below zero.

At any rate, after some years spent in Northern Europe, the most important item for me is a large warm scarf -- something like this:

Because of its exceptionally large area (mine is probably around 3m x 20cm, 100% acrylic, and certainly not the largest available), you can wrap it up very well around your neck, and even the lower part of the face, if necessary, and it keeps you warm and prevents cold air from sneaking in your coat/jacket. From personal experience, this thing reduced the rate at which I get colds or other cold-related respiratory conditions.

You can also wrap the scarf around your face, but you probably wouldn't want to do that except in dire circumstances, as it will attract some questionable looks from the locals.

Finally, this accessory is certainly a welcome addition to any fashionista's wardrobe, and you'll notice that a lot of people are wearing them.

In addition to what has been mentioned here above, make sure you wear layers of clothes. Layer on a reasonably warm jumper, shirt, and a jacket and that will keep more warm than a single heavy jacket over a t-shirt. It also allows you to take off layers if there's sun outside and you start feeling slightly warm, but not warm enough to walk out without a jacket on at all.

I usually go with Jeans, some long sleeve shirt, another warm shirt on top of it and a wind-proof winter jacket. Make sure your boots/shoes are waterproof in case you encounter snow, especially if the temperature is close to 0. The snow will melt and you get water inside your shoes, and nothing is worse than wearing wet socks in winter.

If you get wet shoes anyway then stuff them with old newspapers and put them on the radiator overnight.

Some scarf or headgear that covers your ears is also an advantage in windy areas, mountains or high buildings.

your jacket looks "ok" for maybe 10 Degrees and above, but you should ask in a camping store for proper advice; and not browse the google merchandise store for this sort of trip :)

The jacket is enough for a very hardy person, especially from a Nordic country, who is trying to do some "conditioning." For most people, you need a second layer.

You're talking about a 15 degree difference (Centigrade, 25 degrees Fahrenheit) from top to bottom. That jacket is enough for the top end of the range, but not the bottom (for the average person). You may be one person who's the exception to the rule.

I'm British, in winter most people generally wear jeans, trainers, t-shirt with maybe a jumper or fleece underneath, and then a thick coat.

Gloves and a hat, with an optional scarf (Most big jackets cover your neck enough to do without one, IMO).

You should be good to about -5C with that.

Don't ask me what to wear here though, I just moved to Quebec!