I would suggest it is complicated and there are quite a lot of recent studies which I would suggest haven't yet found all the effects let alone agreed about those effects. See video by Dr Francis linked from
http://forum.arctic-sea-ice.net/index.php/topic,750.msg68965.html#msg68965 first 25 minutes is fairly basic stuff that I think most people here would know about global warming.
Then it gets onto more weather impacts of arctic amplification and loss of sea ice.
To attempt short summary:
Land and arctic warms faster than rest of globe.
Same pressure is higher in tropics than by pole and this drives jet streams.
This pressure gradient is reduced by arctic warming causing a greater increase in height of a given pressure at the Arctic than in tropics or mid latitudes.
This weakens jet stream.
Can cause more wavy, slower moving and increased frequency of blocks.
Causes more persistent weather. So more intense flooding, longer droughts, longer heatwaves, longer cold spells etc.
But it can be more complicated than that for instance interactions with PDO/warm blob/cold blob/El Nino.
This is probably all happening now with just fairly small regions of summer retreat of sea ice. May get more significant with further ice retreat or maybe more persistent changes if it requires interactions to really see an effect or maybe there will be other effects that we haven't realised yet becoming more apparent.