As with so many concepts in geography, I don't think there is a definitive answer -- it would very likely vary from city to city and from year to year. Urban heat island (UHI) effect is affected by so many different variables, such as albedo (reflectivity of surfaces), specific heat of the materials receiving and releasing radiation from the sun, thermal conduction into the ground, cloud cover, wind, and as you mentioned, anthropogenic heat production.
Throughout the year in a city with four distinct seasons, most of these variables change independently of each other (except for probably the specific heat of the materials). For instance, in a hypothetical city that receives a great deal of snow, albedo might be much higher in winter due to the high reflectivity of snow covering low-reflectivity surfaces (such as asphalt, roofs, etc.), which might reduce its contribution to UHI by causing fewer surfaces to absorb radiation from the sun. However, as mentioned in the question, anthropogenic contributions to UHI Effect might be higher in winter in the hypothetical city from latent heat from buildings, water/sewer pipes, vehicles, and so on. Further, wind patterns might shift in winter, bringing in more cool air in winter rather than summer, which would counter the increase from the anthropogenic sources.
Also, impacts from urban heat island are actually generally most pronounced during dusk, which is when much of that short-wave radiation from the sun (which was being stored all day in the sun) is released as long-wave radiation. With that in mind, another factor that could contribute is day-length. Many cities with four distinct seasons are in the mid-latitudes, which have variable day lengths between the seasons. Longer daylight in summer, then, would suggest that the UHI Effect would be worse in summer, as there would be more time for the surfaces to absorb short-wave radiation from the sun.
Great question - sorry for not definitively answering it. It appears there are some gaps and conflicts in the limited research on this topic.
A grad student at UMN suggests that UHI effect is worse in winter (without really explaining why), while TR Oke suggests it is worse in summer, while James Voogt suggests that UHI effect is generally stronger in summer and winter compared to spring and autumn (in the mid-latitudes).