My attic is so hot and I wondered if replacing turpins instead of the square vents I have on my roof now would cool down the attic and is it cost effective?

I think we call turpins "turbines" or "whirly-birds" here.

I do not recommend ever installing an electric exaust fan on your roof because the extreme tempetures which cause the moter to run pretty much constantly during the cooling months, will burn the motor out in 2-3 years. When this happens, you are left with no exaust fan at all. WhirlyBirds operate by the difference in temp between the attic and outside air and have no motor to burn up and will last for decades.

As a home inspector, I've seen about 8,000 attics in 15 years. Wind turbines work well in the summer, but tend to freeze and leak snow/ice in winter. If they get stuck or the bearings go bad they will leak water. Thermostatically controlled fans work well in summer but don't run in winter unless you add a humidistat or manually controlled switch. They don't tend to leak like the turbines. Make sure you have adequate venting around the perimeter eaves/soffits as well. Soffit vents will allow air to enter the attic as it exits the upper vents so make sure they are clear of paint and dirt and insulation.

There are turbine covers on the market. Is it OK to use them in winter to prevent leaks?

Ventilation is at least as important, and probably more important, in winter than in summer, so covering turbines would not be a good idea.