You definitely need a tripod for the northern lights. Set ISO to 1600, shutter speed for 20 to 60 seconds, aperture open as much as possible. Manual focus at infinity. Make adjustments to shutter speed or ISO as needed.
For sunny shots in the snow, set your exposure compensation to +1.5 if you are using P mode (or A or S). The old rule is "brighten your brights and darken your darks." That's because your camera meter will read all of the light from the snow and reduce your exposure, making the snow gray and the people too dark. By adjusting the exp. compensation to add twice as much light or more, you are getting more light on your subject, and the snow should look a true white. If the D3400 can shoot in RAW mode, do that, so you can make better adjustments to exposure in Photoshop.