Yes, you can put milk in your tea straight from the fridge. Whether you add cold milk or hot milk to your tea is a matter of personal preference. Some people prefer to add cold milk to their hot tea because it cools the beverage down quickly, allowing them to drink it sooner. Others prefer to warm the milk before adding it to their tea to avoid lowering the overall temperature of the tea.
If you add cold milk to your hot tea, the tea's temperature will decrease slightly, but it may not be significant enough to affect your enjoyment. It's entirely up to you how you like your tea – some like it piping hot, while others prefer a more moderate temperature.
Ultimately, it's a matter of taste, so feel free to experiment and find what works best for you.