I just got a product announcement from Digi-Key for a new Honeywell Digital Humidity/Temperature sensor IC and it looks to be pretty low-power. Available both as I2C and SPI and has a 14-bit ADC. Doesn't have the pressure sensor that was also requested (so there goes barometric pressure), but may be a possibility for the other two:
http://www.digikey.com/product-highlights/us/en/honeywell-humidicon-digital-sensors/25
http://www.digikey.com/product-highlights/us/en/honeywell-humidicon-digital-sensors/25