Slopes present unique wild fire danger.
Give some thought to this picture if you have anything valuable below, on, or above a slope. The risks of fire include:
Fire moving very fast up slope making it very difficult to prevent total destruction on or on top of the slope.
After the burn, because the soil can become hydrophobic (repels water and does not allow it to soak into the ground) it presents a risk of erosion and even landslide with enough rain and enough soil destruction (hydrophobicity).
There is a risk of objects (wood, branches) catching fire, and rolling down the slope, igniting fire below.
It's important to have all of this in mind when thinning your land.