Fell off my bike twice today

I's not even that cold here: normally if I see my front garden/steps iced up, I won't ride, but this morning at 8am it was fine. I don't have to ride on the roads, I do cycling path cum pavement, park, more cycling path, more park, more cycling path and that's me at work. On entering park N1, a passing dog walker warned me about the ice, so I slowed to 2mph

, got through it no bother, reached the bits with the shops, see other cyclists and stop worrying.
Through the industrial estate: no ice, just slush, away I go. Want to resume my normal 5mph speed, but I desist in the name of caution.
On entering park N2 (Glasgow Green) I had to break a wee bit (back break, I read in another thread that this is the wrong breaks to favor), down I go like a numpty. I was doing all right before using the brakes!! But how was I meant to stop??? I then take to ride the grassy bit, ok until I need to reach the opposite grassy bits ...should have walked the bike, but I am stubborn, down I go again!
After the first fall a gent my age (cheeky sod, what goes round will come round!) passes me on his bike, smiles at me, I tell him "be careful of the ice, I just fell" he smirks and says "I know", away he goes. If he had stopped I would have asked him the make of his tires, the b*****d.

After fall N2, near the exit of the park, had to adjust my handlebars: a couple of lyca cladded young ones (considering racing in the park, bless them) ask me if I was ok, did not want to approach sooner in case I got scared of strange men in Glasgow Green, they said. I reassured them, put my allen key back in my rucksack, exit the park and a road worker tells me to be careful, the path is all ice ....

Reach work without further disasters. All day I see cyclists back and forth the SECC .... What did I do wrong????

Took the train back home, just as well, I think I need new back break pads.
At least I'm not scared of coming off my bike anymore
