I'm going to speak exclusively about the military here, since I studied the Roman Army, but almost no Roman fashion.

Firstly, it's important to recognise that the Roman army did not have uniforms in the sense that we are used to. You could have a diverse range of regional dress even within a single unit.

Even armour was based on what worked best/what you had. Some Roman soldiers would be wearing armour from their fathers/grandfathers' times (as long as it worked it was fine - obsolecence wasn't too much of an issue). Even Imperial armour factories would produce different types of armour based on where they were situated - depending on the resources available in their provinces.

Pretty much the only standardised item was the tunic - although the colour of that tunic would be based on what was available or cheap. While we have evidence of red and white (or off-white) being common in frescoes etc, there was no standard colour.

So if there was no set uniform, what did Roman soldiers wear in Northern parts of the Empire?

Braccae or Feminalia - These were kinds of trousers. Braccae were loose fitting and often woolen. Feminalia were tighter fitting and usually knee or calf length. Originally in the era of the Republic, wearing trousers was seen as a trait only of the Barbarians (since they originated from places like Gaul), but as the Empire expanded, Roman soldiers started to see the use of keeping warm! Wearing trousers never became a part of fashion in Rome itself, but they were popular with soldiers.

The sandals you're thinking of are Caligae (incidentally, where Caligula gets his name from - literally 'little boots'). While these hobnailed sandal-boots were perfect for marching in cooler climates, wet and cold places needed something else. Soldiers in colder climates appear to have worn Carbatinae which were made from a single piece of leather. These still have a fairly sandal-like appearance, but are much more closed. Military ones also had additional nailed on soles. There is some suggestion that soldiers may have packed their Carbatinae with wadding or worn some kind of woolen sock for extra warmth, but evidence for this is lacking and thus is mostly conjecture.

Again, other than the tunic, whatever the Roman soldiers were wearing would depend on what they had/could buy or make/had been given. So there is an almost endless variety of possibilities!

Sources: Graham Sumner, "Roman Military Dress" (A great book for looking at the different kinds of outfits that could be worn with illustrations).

Carol van Driel-Murray, "Vindolanda and the Dating of Roman Footwear". Available on JSTOR, but an account is required: https://www.jstor.org/stable/526955