How do you do this? When I am cold my nipples are really painful. I can't even bear thinking about getting my baps out at the park but I have a toddler as well as a 2 week old ds so I can't stay in all winter!!
I don't normally cover for bfing in public but made an exception when DD2/DD were very small (they were born in Oct/Nov). I used to take their blanket out of the pram with them when they needed to feed and snuggled up with them on a bench if they needed a feed whilst at the park.
Having said that there is a condition called Raynaud's Phenomenon that can cause pain when the nipple (or other extremity) is exposed to cold air.
You can do things like keeping a cloth breast pad in your pocket or somewhere warm like between your legs when feeding and putting it over your breast as soon as feeding stops. The hand warmer packs might work too but I would check out how hot they get before sticking on down your bra!
The classic 'Two Tops' method of feeding might help too - you have a vest top with stretchy straps/neck line under your normal top and you can get ready for a feed by dropping bra cup/pulling vest under breast before you lift the top so minimising air on the nipple. If you tuck the under top into your trousers/skirt you can keep a bit warmer that way too.
You also might be able to get thermal vest that you could modify to allow bfing (most wouldn't have stretchy straps) by cutting slits in the front though if it was really cold you could have 'Three Tops' by layering your bra then thermal top with slits then vest top that can be pulled aside to access the slits then your ordinary top over it all.
My DD was born last October and I did the two-tops (plus a cardigan) all winter. I also used to keep my bra on the radiator when I had a shower so I could dry off quickly and put it on nice and warm!
I found the painful/ cold nipples thing did go away after a while, one of those getting used to breastfeeding things I guess.
And as far as having a 2 year old and a baby -- yes, actually you can stay in all winter. At least as far as feeding is concerned, just feed her indoors. Just time your trips to the park around feeding and/or don't stay as long.
Or just don't go. Don't feel you have to drag your infant out in the cold just becuase you took your toddler there before you had the baby. There will be plenty of park-going time when the baby is older, the weather is warmer, and you've had some sleep!