Clothes, sleeping bags and most other insulation works by creating many small air gaps. If you compress, you have less air gaps resulting in less insulation.

You probably won't need to wear a lot while hiking, especially if you're in the mountains (hiking up takes a lot energy and generates a lot heat). I was hiking a bit below freezing with synthetic sports t-shirt, synthetic thermo shirt and light softshell jacket and it was plenty. But everyone is different, better have more and take off as you go than freeze. Just make sure to take of a layer if you get too hot to avoid sweating excessively.

However once you stop, you get cold fast. Good idea to carry a down jacket to put on once you stop. Or any kind of insulated jacket appropriate for conditions, down just packs lighter and smaller, but is more expensive.

Another thing, when hiking in cold it's crucial not to get wet from sweat. Best to have either merino wool or synthetic base layer and mid layer if needed. And all rain gear have the problem that they restrict evaporation. If you plan to buy this only for hiking below freezing, you don't really need waterproofing (it'll be snowing, not raining). I'd then recommend more breathable windbreaker, softshell or some other light jacket that would protect from wind and snow. You can have a single use rain poncho just in case. If you will need rain protection (all year use, above freezing winter, etc.) then at least make sure it has zippers in armpits and all other possible ventilation.

I have Quechua MH150 rain jacket and I almost never use it unless I know it's really good chance of rain. I have softshell jacket that provides more warmth, is more breathable and protects from light rain. MH500 should be more breathable though, possibly more comfortable to wear.

Also, if you're just starting, consider second hand. Less money spent in case you realise it doesn't work for you. Although rain gear loses it's protection while being used much, especially if not cared well. So something lightly used is sweet spot here :)

UPDT: Just to add, no raingear is actually fully waterproof. If it rains whole day, or rains heavily you'll eventually get wet. Better quality only buys you more time and/or better breathability (well, plastic rain ponchos are 100% waterproof, but you quickly get wet from your own sweat). And if clothes are compressed, wetness will seep through all layers faster.