Which is harder on the power grid: a winter cold spell, or summer heat wave?
You don't define what you mean by "harder".  In New England, the hardest time on the grid is in deep winter.  The region is summer-peaking in terms of electricity demand, but political and structural problems cause the cost of electricity to go much higher in winter.

The basic problem is that the supply of natural gas into New England is limited, natural gas is a major fuel for winter heating, and by law residential heating customers get first dibs on the limited supply.  This means commercial electric power plants can't use natural gas as a fuel on cold winter days because there simply isn't enough of it.

The bottleneck isn't the overall supply of natural gas.  Plenty is being produced in North America due to fracking technology.  The problem is getting this abundance into New England in sufficient volume.  The existing pipelines are too small for the demand on a cold winter day.  Years ago before the fracking boom, liquified natural gas terminals were built in Everret MA and someplace in New Brunswick or Nova Scotia (sorry, don't remember the details).  More pipeline capacity overland was not built because there wasn't any excess gas in the rest of the continent to get.

Now with the technology advances that allow extracting vast quanties of natural gas from places like the Bakken formation (more oil than all of Saudi Arabia, but a lot harder to extract) and others in North America, there is suddenly a glut of natural gas at the other end of a thin straw from New England.  When available, this gas is much cheaper than LNG brought in by ships.  Also, LNG has to be planned on ahead of time, whereas with a pipeline you just turn on the spigot.

Despite a unusually cold last winter, none of the electric producers took the risk to order ahead the available but more expensive LNG.  By the time it's cold, it's too late to arrange for a ship to show up in time.  A contributor to this is that ISO-NE (the quasi-government agency that oversees the power grid here) discouraged commercial electric generators from arranging LNG.  This may sound backwards, but they want new pipeline capacity built, and want to deliberately create more of a crisis than necessary to get the public to support the new pipelines.

My town has a municipal electric company, as apposed to being served by one of the large investor-owned utilities like NSTAR and National Grid.  Up until this year, we kept the price constant over the year.  This meant we lost money in the winter and made it up in the summer.  Last spring, "strips" (wholesale blocks of electricity contracted ahead of time) for January 2015 were selling for $.18/kWh, which is considerably more than our electric department sells it back to consumers.  The spot market fluctuates much more widely, and last year hit much higher prices than $.18/kWh during peak demand times when the temperature was low.

This high winter price is solely due to unavailability of natural gas.  Some producers have to shut down when there is less gas, and others switch to more expensive oil.  Note that the expense here isn't just the oil, but the regulatory cost of burning more carbon to get the same energy.  In summer, the wholesale cost is more like $.05/kWh or so, even during peak electric demand that exceeds the peak electric demand during winter.

But wait, it's even more messy than this.  Generation capacity is actually being reduced in New England.  The coal/oil plant at Salem Harbor has already been shut down, and the large coal burning plant at Brayton Point is scheduled to be shut down.  These were done for environmental reasons, or more accurately, higher costs created by environmental regulations aimed at reducing carbon emissions.  That may make some sense, but the generating capacity is not being replaced.

Not only are some large carbon-spewing plants being retired, but incredibly, the Vermont Yankee nuclear plant also.  This plant was functioning perfectly well, and of course wasn't producing carbon emissions.  Other regulations made it too costly to keep operating to the point where the owners decided that shutting it down was the best choice economically.

Yes, this whole issue is quite a mess, with lots of different groups pulling in different directions with different purposes.