There isn’t one right answer.
Some things to consider when taking on a remodeling project;
Summertime:
Summertime is a great time for the weather, longer light hours but it also means contractors are busier, hotter temperatures and long sunny days might not be the best for some projects.
Here are some projects that would work well in the summer months.
Springtime
In the spring the ground is softer and easier to build on, working projects in the spring also means cooler temperatures for workers, and the outdoor space will be ready to use in time for summer so getting those projects done like a deck/roof/cleaning/AC Duct work/replacing windows or adding insulation are good to start in spring.
Fall
Rain can be a problem in fall, however cooler temperatures and dry air make fall an ideal time of year to make renovations. Many contractors are starting to wind down for the year and focus on inside projects, so fall may be the perfect time to get into their busy schedules depending on where you live.
Winter
Colder months can be a great time to get many projects done, whether it is hiring a contractor or doing it yourself. Winter can bring savings on costs and give you the time to get those time-consuming tasks done like painting, a remodel and focusing on indoor projects. The added benefit of winter is building materials are often less expensive due to lower demand and slower work for contractors which can open your budget to work on various projects at the same time.
References: Home Advisor and Angie’s List
Some additional resources: