Can I add a sub-panel near the main disconnect outside my house?
You can do it -- you'll need a subpanel loadcenter in a NEMA 3R enclosure, though, as well as watertight conduit/raceway and fittings for the outdoor runs, which will be done using THWN in the conduits.

You will want to put a 30A 2pole for the dryer and a 20A GFCI for the laundry outlets, as well as a spare 20A breaker (if you want a lighting circuit there, or an extra laundry outlet circuit) in your subpanel, which does not need a main breaker of its own, so it can be a four-slot NEMA 3R loadcenter, such as an Eaton BR48L125RP with a GBK10 ground bar in it, as the neutral and ground will be on separate, isolated bars in the subpanel.

As to the feeder breaker, the NEC calls for 1500VA for the laundry outlet circuit (220.52(B)) and a minimum of 5000VA (a 20A dryer) or the wattage of the dryer (whichever is higher) for an electric dryer load (220.54).  Assuming your dryer pulls the full 30A (7500VA) and you have 1500VA of laundry circuit load, this yields 9000VA or 37.5A, which requires a 40A feeder breaker in the main panel, and 8AWG THWN for the feeder wires.  In reality, your dryer can't sit there and pull 30A continuously without tripping your breaker, so this is a conservative calculation.