@Yellow Saddle I would be interested to hear what tyres you use on your bikes in winter. I'll state that my main concern in winter is not speed/efficiency, but staying upright and mobile. (Changing tyres in freezing conditions is a nightmare)
Ice can be harder than the tyre I imagine. What are your thoughts on studded tyres in icy conditions given that most studded tyres also have tread pattern? Does the tread deduct from the performance of the tyre, in order to be marketable to a gullible public who believe tread is best? The tread on marathon winters for example is too shallow to help with navigating snow. Also, I'm under no illusion that the tread helps with ice, that'll be the studs.
Am I better to switch from 35mm tyres to 28mm studded tyres in deep snow?
I don't change tyres for winter but use the same smooth tread tyres all year round. However, I avoid black ice because I have other options when the roads are iced. Nothing but studded tyres will work on black ice.
Don't worry about the tread pattern on the studded tyre. They're there for perceptions and deception and I would imagine that you won't find a smooth studded tyre in anyway. If on the other hand, the treads are very aggressive then the tyre could be of benefit on both iced roads and mud. But I doubt it, because the studs need to be mounted on firm rubber. Do you perhaps have a photo of what you have in mind?
The tread deducts from the performance of a tyre in several ways, all or none may be applicable to your type of roads. Inverse tread on tyres intended for tarmac roads increases rolling resistance but not cornering ability and slightly reduces durability. Lugged tread reduces steering ability, increases rolling resistance massively and of course, adversely affects durability.
In deep snow, I doubt a couple of mills will make a difference. There will be difference between a fatbike tyre and a 23mm, but I can't say what because the term deep snow is ambiguous. Perhaps the snow is firm enough to allow the tyre to float, perhaps not, etc etc. I'm sure you see the number of variables one can dream up. If you currently have studded tyres, just stick with whatever they are, you won't improve things by throwing money at it.
Winter tyres for cars make sense if your winter conditions are persistently in the 5 degree C region and below. That's not because car winter tyres can grip on ice - they can't. Nor is it because they have more aggressive tread. They grip better on asphalt because they are softer than summer tyres used in cold conditions and a softer tyre squeezes into microscopic road voids better than a hard one. The aggressive thread helps to make the tread squirm more and again, it then "finds" more voids in the road to fill and switch on the adhesive force, which is Van der Waal's.
If the tyres are designed for snow, they will be narrower than the car's stock summer tyres to cut through the snow.
It is an exact science but applied to very, very inexact and inconsistent conditions.