Well the Earth`s cycles may include dryer weather for a spell globally and fires will increase. I doubt you`ll change Summer into Winter like 1816 because that was volcanic but you will get warm currents going under Polar shelves and that results in rising sea levels that will be blamed on man made global warming.
Now I don`t remember such large forest fires and the scale of them ,from the 70`s 80`s and 90`s but I do remember a lot from the last 14 years so maybe what`s supposed to happen, is happening and what`s not gonna happen, isn`t.
normal forest fires do cause localized cooling (after the fire is out, but before the smoke clears)
the smoke can disperse into the enormous volume of the atmosphere, even with no wind, heavier particles can settle out, wind can disperse it faster, smoke particles can form "nucleation sites" to grab shittons of humidity and drop it to the ground as black rain (seen it) which can stop a normal rainstorm from doing it's thing, and sometimes geographic features can trap smoke and make it hang for weeks or even months (again, look at the LA Basin, formerly known to the natives as "the valley of smoke")
lets look at the LA basin's thermal layer:
http://www.umich.edu/~elements/web_mod/la_basin/background.htm
in brief: the surrounding mountains form a bowl with only one outlet, the sea shore.
mild onshore winds through almost all of the summer months stop up the ocean facing outlet but rarely penetrate more than a mile or two inland due to the Thermal Layer
the Thermal Layer is a dense high pressure zone caused by the surrounding mountains and the shape of the basin, causing a Hot Pot effect winds from the sea cant get in, and a high pressure inversion layer above the basin corks the top, so when theres a fire (pre-Los Angeles) the smoke would be trapped for weeks, and even months (hence "The Valley Of Smoke") until the santa ana winds come in and blow it all out to sea around late august to early september. these winds can breal the Hot Pot, cuz they are strong as fuck, if you never been there you have no idea what im talkin about. it's unreal. sustained winds of ~35 mph, for days or weeks on end, heading out to sea from the desert.
if you get on a bike in camarillo, you can ride all the way to oxnard (20 miles or so) without pedaling, the wind just pushes you along at around 25-30 mph the wind can even blow you up hills.
the santa anas make the powerlines resonate and sing like a harp, thats what it takes to break the thermal layer's grip.
and it's all natural.
now however heat from concrete, asphalt, industry, cars, and even just all those people breathing has made the thermal layer even stronger, and the Hot Pot even tighter.
ordinary auto exhaust, smoke, dust, some ozone, methane, etc get bottled up, accumulate in a huge cloud of the infamous "Smog" and it stays in the air until the santa ana winds, infrequent rains or an unusually powerful high pressure zone from the tropics comes in to wash it away
IF however, the entire globe is covered in smoke, theres no less smokey air for the smoke to disperse into, smoke strips the humidity from the air by grabbing the water vapour before it can form rain, and drops it as "black rain" leaving the air still full of smoke, and breaks the normal weather cycle by making the whole planet less warm, and less cold, depending on the lattitude
this changes the pressure systems too, so instead of High Pressure Zones and Low Pressure Zones meeting to make storms, you got pretty much one giant "Medium Pressure Zone", and like a fart in an elevator, the smoke just lingers.
or so the global forest fire nuclear winter theory goes.
lets not test this one.