Good advise thus far so use what is most comfortable for you! Here is what I would do... saws and routers are good options to start your needed cut because they can be accurate, but you have physical obstructions preventing you from completing the finished cut... If you can, I would start the work with a router and be almost accurate. Take a proud 3/16th off with the router as far into the completed cut as possible. Finish that almost perfect with a good sharp chisel by sliding the flat back side of the chisel along the surface of the almost perfect (a bit proud) cut. Then use a flat metal file to sneak the final cut down to your desired perfect need. I always use this method for my MT joints.
Its' never hot or cold in New Hampshire... its' always seasonal.