Investigator... helps both your bad saves, keys off the only mental stat you have a positive modifier in.
around 11th level is the perfect time for the archer to pick up two weapon fighting. You should have pretty much have all the relevant archery feats by then, and should have a high enough DEX to qualify for all the TWF feats.
If you are set on going with a different class, pick one which has synergy with TWF (Barbarian and rogue both come time mind). But YMMV.
Also, the Dragon's Blizzard effect just states that it it heavy snow and reduces visibility as Fog, and the Conditions table has Heavy, light and medium fog, since the ability doesn't specify, I would have ruled that it would be medium fog, which only reduces ranges, not acts as the fog spell, which would limit you to 5'. (so IMO, you should have still been able to use archery)
However, having something to switch too when ranged combat doesn't work, is always a good thing.
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You might want to look at one or two levels of Rogue. This would give you a 1d6 Sneak Attack bonus if you have achieved Ranged Flanking.
A second die of Sneak Attack would be available via a feat.
The second level of Rogue would give you Evasion, if: your Mithral breastplate counts as light armor. A Mithral armor counts as one lower armor type for most purposes, but I don't remember if this applies to Evasion requirements (I believe it does, but I'm not sure).
You don't appear to have a melee weapon...which suggests that without the bow you are going to feel a bit useless. I'd dip a level of (Urban) Barbarian (+10' move, rage, skills) or Bloodrager (+10' move, rage, wand use, skills) or maybe Ranger or Slayer. Maybe even Paladin to do something about that horrific Will save. And take either Power Attack or Iron Will.
Archery is great when it is, but when it isn't, you need to be able to do something else.