Since both developers and high-reputation forum members have failed to provide a complete solution for restoring the good old icon of Sublime Text 3, here is a handy script that will do the job.
Copy-Paste this script into an .sh file and start it with sudo.
#!/bin/bash
# Create and change to temp directory created
extract=`mktemp -d`
cd "$extract"
# Get Sublime version 2 (it has the old icon set)
wget -c https://download.sublimetext.com/Sublime%20Text%202.0.2%20x64.tar.bz2 -O sublime.tar.bz2
# Extract the icon folder
tar jxvf sublime.tar.bz2 "Sublime Text 2/Icon"
# Change to the extracted directory
cd "Sublime Text 2/Icon"
# Copy all icon files into their proper system folders
for size in *x*; do
cp -v "$size/sublime_text.png" "/usr/share/icons/hicolor/$size/sublime-text.png"
cp -v "$size/sublime_text.png" "/opt/sublime_text/Icon/$size/sublime-text.png"
done
# Clean up
rm -rf "$extract"
You can run this script on each sublime upgrade to get the old icon back.