White winnie (WW) is not the best aggro deck in peasant. Affinity is. But White winnie, with the recent additions from the Time Spiral block, has found some solutions to most of the gauntlet decks.

Ramosian SergeantThe best peasant version is a Rebel engined WW, designed - again ! - by Christophe Deslandes, the Rebel mechanic providing the library manipulation and tutoring you might need.

20 Plains
4 Bonesplitter
1 Defiant Falcon
1 Whipcorder
3 Amrou Scout
3 Zealot il-Vec
4 Benevolent Bodyguard
4 Children of Korlis
4 Crimson Acolyte
4 Icatian Javelineers
4 Pegasus Charger
4 Ramosian Sergeant
4 Swords to Plowshares

Sideboard
4 Dust to Dust
4 Holy Light
4 Rune of Protection: Red
3 Divine Offering

It can deal with Affinity thanks to Pegasus charger (blocks a plated orni withouth dying, thanks to First strike), Whipcorder (by tapping the big Atog), and post side, with Dust to dust and Divine Offering (both spell will help against any heavily artifact based deck).
The classic RoP : red cuts Burn strategy out. Crimson acolyte doesn't help Burn nor Gobs, and it can be replaced with Obsidian acolyte (although a good build of Mono black should play Diabolic edict, and thus, don't fear the acolyte ability).
Decks with numerous creatures can be halted with your own hordes, and their abilities (Zealot and Javelineers are plagues for Gobs and Elves) and post side, Holy light can stand the Wrath of god slot.
On top of all these, you can use your Swords to plowshares to gain tempo. Against Affinity, it might be all that you need (hard to come back with an empty hand and an empty board after your 'tog's been "sworded").
Children of Korlis is probably the best answer you can afford to damage-based combo deck, and good news, it's a rebel !

Once you've dealt with menaces, you can use your own, that is, basicaly everything able to swing a Bonesplitter (sorry, no Jitte allowed in PEZ...)

WW might be a good deck to play if you don't know what your metagame is made of. As it is very polyvalent, it's also a good testing deck : everything loosing too many times to that deck should worry (although there is a most definitive test deck, that we'll discuss later).