ESP8266s go for $1 SE Asia, and down to 0.50, or less in quantity.
Different sleep modes can be programmed and the thing can run off a very small solar cell or a coin battery for a year or two depending on WiFi usage, etc...
You can program to the metal too, if you want low-latency.
Except ESP8266 is not usable unless you're somewhat proficient with electronics. Basic Arduinos you can hook up via USB. Yes, there's NodeMCU (which I very much like), but unfortunately it's not $1.
What's not $1, the arduino or NodeMCU (opensource)? The price I quoted was for board with power regulator, breakout of GPIO, and WiFi (of course). You can run the Arduino IDE and serve web pages from it. Someone has created a Lisp/scheme running on it.
I've been tinkering with the ESP8266 since it came out and best board I've found so far for hobbyists is the WeMos D1 Mini. It's based on an ESP8266EX but is mounted (everything except headers are soldered) on an Arduino style breakout board with a USB-serial converter. It's $4 at retail prices from AliExpress which includes shipping.
What do you mean 'not as deep as the arduinos'? There are definitely issues with coordinating WiFi and low-power usage requirements, but it offers several low-power states, that I have not had issue with so far.
