Though two items I would advise against scrimping on if you are planning to spend a bit of time in the snow.

Gloves - Cheap gloves fall to pieces quickly, and over time will cost you more than expensive gloves which can last forever. Cheap gloves also have a nasty habit of the liners pulling inside out if they get a little damp either from the snow or sweat and being impossible to put back on again. Get gloves with removable liners if possible as they are easier to dry overnight.

Boots - Not that there are really any bad boots on the market these days. What you are really looking for is a good boot fitter who measures your foot, length, width and arch height, lets you try a selection of boots rather than a fitter who stocks only one or two brands and scientifically asks "So, how does that feel?". Take shortcuts here and you will pay for it in other ways. If you are planning to go away on a skiing holiday, buy the boots at your destination so that if you have problems during the day they can sort them out overnight. If you are doing weekend trips locally then buy them somewhere that you can take them to be worked on during the week.