I highly recommend one. I am not sure where you are, but in the US the winter sun is too weak to sustain compact growth this time of year, even in a sunny window. You will end up with leggy, weak seedlings. All you really need is a clip-on light (~$7) with a 27w or so CFL. Put it pretty close (within an inch or two) of the seedbed.

I have (and am) successfully grown plants in natural winter light that don't require a lot of light. I have an upward facing dome for this. This includes lettuces, basil and other herbs. Light loving plants such as tomatoes and peppers will not do well in a window however. You need to supplement with fluorescent light. An energy saving compromise is to put your light when it is dark outside to extend the hours of light, or keep it on daytime as well for faster growth. My recommendation is to use T5 or T5HO's for seedlings. CFL are fine if you don't have many plants, but the T5HO's are best when you have multiple flats.

I totally agree that winter sun leaves a lot to be desired for germination and cuttings. With a shop light [grow light is not necessary] I can control the amount of hours seedlings have light. For germination purposes on seeds leave the light on 24/7. Once you have sprouts they still get 14-16 hrs of light. Here's my little brood currently.

mostly salvia guaranitica and cuphea david verity and micropetala

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To start, I'm in Ontario where I have MUCH less sun than you do, and I started annuals in a west facing picture window last March to transplant into planters in mid-May. I knew nothing about starting plants indoors and also didn't have any heat mats to assist with germination. House temperature was 68-70*. They did great! I just set up my husband's saw-horses and put a 6 x 4' board on the saw-horses and had about 200 jiffy pots. The only plant that didn't do well was pampas grass. I had the most glorious pots on my stairs when they were transplanted. So, YES, it can be done.