Winter tyres are designed to work below 7’C, with grip increasing as the temp drops, the sipes in the treat designed to ‘grip’ the snow, and yes in snow/slush conditions they do work, and they are better on icy roads.
However on reasonably cold wet roads, which describes the UK road network for the majority of winter, and especially where salt has been laid for several days and then gets damp and becomes mushy, you can find those expensive full winters not as grippy as decent normal tyres.
Answering your questions.
Not really any noisier but those sipes can set a sort of buzzing noise up on dry tarmac, its not loud or unpleasant in any way.
It’s not the best cost time to get winter tyres, the time to get those is in the spring and early summer when prices fall drastically.
You should not mix winter and summer tyres, because the grip values will alter considerably depending on conditions, if you put 2 winters on the drive axle you’ll have more grip from the other end in the dry/wet, and then the grip will alter when its gets freezing, if you go on Youtube there’s some interesting videos showing what happens when they are mixed, scary stuff.
Full winters used all year round would wear quickly in the summer and give very disappointing grip in the warm weather.
Much depends on what sort of car you have, and more importantly what tyre size you are on, if you’re on elastic bands (ie 30/45 aspect) the chances are they’ll be bloody hopeless in snow, if you’re on more sensible stuff like 55/65 aspect then more likely to reasonable.
My own suggestion of you’re changing tyres anyway is to go for decent all season, such as Michelin Cross Climate or Goodyear’s equivalent, and i’ve also had very good results from Vredestein Quatracs over the years, and near enough half the price of the Mich’s.
By the ways genuine all season tyres comes with the snowflake and mountain symbol, some tyres are called all season but do not have this stamping, they are therefore not winter rated and their all season rating is ■■■■■■■■.
Some people confuse M&S with all season, all M&S means is that a higher percentage of the tread is open than more more slick normal tyres, it has no bearing on the rubber mixture or cold weather rating.
If you would prefer to stick to normal summer tyres, the best all rounder in the wet i’ve ever found have been Uniroyal Rain Experts, these are nearly as good as all season tyres in the winter in my humble opinion, Rain Experts become RainSport as the aspect ration drops, ie if you have 45 aspect tyres then it will be Rainsports, these are not quite as good as the Experts in the snow i would suggest, but that is only my opinion.
Thay don’t last everso well but cheap as chips (Camskill have the best prices on these) and the wet grip is worth it.
I take tyres seriously, personally i run all season (snowflake stamped) Yokohamas on my 4x4, these are brilliant in all weathers, like the proverbial to a blanket in the wet, but can feel a bit ‘squashy’ in hot dry weather, but its hardly a sports car so i can live with that minor gripe.
The Mrs rather faster AWD thingy (a bloody flying machine) i have just swapped onto the winter set of wheels/tyres which came with her previous same make car, not too sure about how they are gripping tbh (though absolutely fine on her previous heavier car) and it’s highly likely those particular winters will be coming off and a set of all seasons or Rain Experts going on.
There that’s clear as mud innit