Nothing wrong with riding slowly and carefully! And I trust your tyres were fresh and good.
-repeating what many said: it is wet and it looks very slippery. It is obviously also chilly (less than 10 degrees?) and most importantly: as you ride very slowly (have ridden until the issue on this low-speed track?), your tires (front tyre) are simply "cold as at the pit". **I quite strongly think**
A throttle control attempt with low gear and "with only the smallest extra" could equally well have caused your rear wheel to slip, followed by a lowsider.
On such a snail-speed track under cold rainy conditions and without heaters, I think only lowering the pressures of tires might be helpful: To get the tyre temperatures to raise to the minimum during the warm-up lap(s).
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Edit: When driving faster and cornering using some acceleration it is OK and even required to move weight on the front wheel - all with your head and body. (-this as a reflection to some earlier comments.)
The grip in the "larger" backwheel isn't better than in the "narrow" front tyre as the contact patch area only very, very little affects the grip (i.e. into the friction co-efficiency). And the area doesn't even impact linearly or in the way many may think. For such low speed circumstances, you can lower the pressure in tyres: the contact patch areas gets larger but that doesn't worsen the grip per se. The tyre bodies will get some more flexible, but you will not need such a stiffiness or stability for low speeds; hardly no risks for wobbles or such. Importantly you may be able to reach the normal or at least the required minimum working temperature for the rubber. Being the pre-requisite that you can start "driving" and cornering, by first feeling some grip under you..
I hope the damages on your bike were just cosmetic (this is what the crashpads are for!), and I hope this all just encourages and determines you to continue, on all kinds of tracks and circumstances.
