Replace the entry roof with a front gable so water and snow aren't dumped on the steps and it looks like a front entrance.

Ditch the octagonal window, maybe a small square one would add some character. If a window is that unusual it should be a lot more elegant or just simple and quaint.

Add a really nice (expensive) carriage house garage door and don't paint it white.

Lower the second floor window sills.

Paint the brick Benjamin Moore "cottage red".

Put some better insulation at the roof eave to prevent ice dams.

I agree with all of mightyanvils suggestions. The entry could easily be improved by just change out the roofline and removing that window, making it a larger one more appropriate for the style of the home. Some paint to differentiate the base of the house from the upper floor and changing out the garage door would all improve the house.

I would be more concerned with those icicles hanging down. These may be an indication that heat comes up through the attic, melts snow on the roof, and the snow freezes on the eaves. This leads to ice dams, leading to backed up water going down your walls & ceiling. Closely inspect the ceilings and walls near the exterior for evidence of previous water damage repairs. The snow on the roof is still there, although the picture may have been taken immediately after a snowfall. Drive by the house a day or two after the snow and see if the snow is still on the roof - if it has melted off near the top, then ice buildup may be occurring. Ice dams are no fun - they lead to perennial spring water damage repairs.

I guess I'm less ambitious than some of the others - I don't think it's all that bad as is, other than the "blueness" of it. How about a beige color for the bricks to contrast with the blue siding. Not too light (to keep it from looking top-heavy) but not brown either. Red seems like too much "in your face" for this demure style of house.

Neither do I have problem with the octagon window, though I would put some kind of high shrubbery or other landscaping under it to give it some punctuation as a point of interest.

I think I agree with mightyanvil about the upper windows - they could use some more heft on the trim. Maybe a relatively inexpensive upgrade would be to lose the shutters and re-trim those windows with a width more similar to the lower windows. You could include a wider lower sill trim board, or under-sill panel to achieve the lowering effect mightyanvil mentions.

I also agree with the others to check into the icicle issue. In addition to the comments others have made, check into air leakage into the attic, such as around plumbing chases, bathroom vents, wires and other small openings. These can result in a large amount of warm air getting in there and melting the snow.

It's a nice house. If you like the neigborhood and the interior(which is where you'll live) I'd go ahead and buy and live in it for awhile. If it still bothers you it can be changed very minimally if the amount the color is that important to you. I think it would be foolish to pass up a house you liked because you didn't care for the way the exterior was painted.

I'd tone down the blue to a good gray. Then I'd take off the shutters, add to the trim,and put real shutters on in their proper locations (so they can close over the windows) with real shutter holdback hardware ( those nice 's' shaped pieces).
I would take out the little bump-out on the porch with the octagon window ( what is it inside? a closet too small to use?) and extend the porch and its roof all the way across to the garage, so you could just park the car and walk onto the porch and into the house from the side ( no snow down your neck). Then add a fence in front of the porch, some nice planting in front of that and a low key front walk (stepping stones?) for people who come by foot.
The upstairs windows could have better proportions, but I'd want to change all the windows, make them all graceful - major remodeling.
If the garage door had any moulding, any shadow at all, it would be much better. Or if just the trim was white and the door itself was a slightly lighter color than the house,it wouldn't stand out so much.
Yes, first check about the icicles - at least know what you are buying!

sorry, in my mind,I had more space between the entry porch and the garage.
Still, I like my porch idea. I think I might extend it to the other side and make it symmetrical on the house...

Is the chimney painted blue, too?

I'd paint the whole house a diff color and be done with it for a while. Then after living in it for a while you will know what you want to do. I too think the windows could be spruced up now or later

I bet the attic has almost no insulation