Looking at the nerfs from an Arena perspective:
Ironbeak Owl: Nerfing its mana cost does more damage than nerfing its stats would've (since it usually died easily anyway), but it'll still get drafted over trash and when desperate for any kind of removal. Combined with the KOTG nerf, should mean Silence is noticeably rarer in Arena.
Big Game Hunter: Doesn't affect Arena much since it's an Epic and nobody played around it anyway. At 5 mana it's only useful in top deck wars or when it gets to kill something so it will be significantly less valued.
Knife Juggler: Huge nerf, since at 2/2 it straight loses to any 2/3 or 3/3. Only really want it to combo with Unleash or Muster now, so it won't be seen much. Less chance of curving out properly as a result.
Leper Gnome: Was never good but is now worthless outside super aggro drafts.
Arcane Golem: Much worse. Before it provided reach or removal, but now it's just an overstated 3-drop with a crippling drawback. Consider that Dancing Swords is considered a poor 3-drop, and it's drawback is delayed via deathrattle. Probably undraftable. Rares get worse.
Molten Giant: Undraftable, I think, but as an Epic it changes little anyway. How often can you actually limbo to below 10HP without dying in Arena? Mage and Rogue, with their strong reach, are way too popular to get away with that often.
Hunter's Mark: Still good.
Blade Flurry: Probably the most important of the nerfs from an Arena perspective. Rogue loses its best board clear and a big source of reach. Well, okay, at 4 mana it's still good for clearing the board, but you definitely need to draft good weapons/spells to make it work, where as right now there's always the fall back option of just using the Dagger for an Arcane Explosion. Significantly hit to Rogue's ability to swing the board and come back.
Keeper of the Grove: Huge nerf. Silence is rarely super valuable in Arena - you normally pick the damage. You better do something good with the 2 damage because 4 mana for a 2/2 is awful. Still versatile so I expect it to see play, but should drop a lot in value now that it can't dominate almost all 2 and 3 drops and regularly go 2 for 1.
Ancient of Lore: Being an Epic it doesn't matter much. Still a strong card to draft, but less of a catch, and less of a topdeck king. I'd rather have AoW every time.
Force of Nature: Epic, as above. No longer acts as reach or removal, but still draftable. Three 2/2s on turn 5 is awkward though: your opponent is likely to be able to trade favourably if they have a board. Will only be great with synergistic cards like Stormwind Champion, Power of the Wild or Cult Master.
Master of Disguise: Changes little. Still an average 4-drop with an occasionally useful battlecry.
Overall, Rogue and Druid get hit. Curving out gets less common with Knife Juggler's demise, which favours classes with good 2 drops. Cards like Arcane Golem and Ironbeak Owl are stronger in aggro drafts (typically Rogue and Hunter). More good news for Mage.
