"They aren't pretty but they do a job," declared the mechanic in my local bike shop. He'd just sold me a set of mudguards using a novel sales pitch that included "they all rattle", "you learn to ignore the sound of leaves stuck in them" and "just hope you don't puncture that often". I paid my money and left feeling like I was wearing a dirty mac and exiting a shop with blacked out windows. Once upon a time I had ridden in all weathers and happily swallowed the spray from the wheel in front because that's what real cyclists did. Merkcx, Kelly, de Vlaeminck - not only did they use the dirt from the road for extra calories, they did it wearing shorts even in winter. Our club was full of elder statesemen who decreed that the young upstarts without mudguards and flaps would have to ride at the back of the group for the comfort of others. Comfort? Why did they even ride a bike if they were looking for comfort!
Between the hardiness of youth and the comfort of later life lies the Ass Saver. This is a mudguard that you clip beneath your saddle. It protrudes a few inches aft and keeps spray off your rear end, prevents that dirty stripe up your back, but offers no protection to the rider behind you. It's the ulitmate in solipsistic design. Like sticking two fingers up at the poor soul being waterboarded in your slipstream, only more aero and not against the Geneva Convention. Despite its limitations as a mudguard, the Ass Saver is a huge success. Little suprise given that people across the globe are becoming more self-centred.
Off road, the hors d'oeurves thrown up from a wet trail will help you cycle quicker for as long as it takes you to find a bush to squat behind. There's no easy way to say this but often you are quite literally eating S-H-*-T. Mudguards are essential on a mountain bike during winter. Not least because mountain bikes are much more complicated affairs than road bikes, with expensive suspension. Mudguards slow the inevitable destruction of seals and bearings. They still aren't pretty, they offer no protection to the rider behind you, but they didn't fall out of the same ugly tree as a set of leaf catchers on an aero road bike. Plus, when it comes to removing and installing wheels a crud catcher style mudguard on a mountain bike will not get in the way.
Of course, the best way to avoid to avoid problems with mudguards making wheel removal difficult is to ride on a turbo trainer reduce or eliminate punctures all together. Tannus Armour provides up to 15 mm of puncture protection to your inner tubes. It can be used with tyres from 28 mm width, so will fit even older road bikes, and prevents around 90% of punctures. For 100% puncture prevention you could try Tannus Airless tyres on your winter bike. They're guaranteed to last 5,000 miles and for 700C wheels come in sizes from 23 mm up to 40 mm.
My younger self would most definitely not have approved of all this puncture prevention. That in itself tells me it's a good idea.