If the range of gravity abruptly shortens from infinite to mere 10 light minutes, assume no other changes in properties and this effect occurs at no time at all. What happens beyond the Sun's gravitational drop-off?
Solar systems don't even form.
Ten light-minutes is barely more than the radius of Earth's orbit around the sun. Assuming gravitational effects have always been short-to-medium-range phenomena no celestial body large enough to initiate stellar fusion would ever form. The accumulation of matter in gravity wells from the supposed "initial condition" of a baryonic soup depends on the attraction of gravity accumulating over much larger distances than this.
1- The Universe Would Be Cold ... And Dead
Considering that solar systems have planets at distances of several dozen light minutes (Earth is at 8:20 while Jupiter is at more than 40 light minutes from the sun), the solar systems, as know them, would never form. You might think that Earth-like terrestrial planets would still form around stars, but that would be impossible. Read ahead.
Galaxies have lengths of dozens of thousands of light years. Limiting gravity to mere minutes range would mean that galaxies never form at all. Without going into lengthy details, let it suffice to say that supermassive blackholes of galactic centers never form at all, putting galaxies out of the picture completely.
Which means that after the Big Bang, universe would go on to expand at nearly the speed of light. Once the individual particles are more than 10 light minutes away from one another, there would be no way for them to ever reunite.
The universe would just be composed of infinitely small, infinite number of sub-atomic particles, moving away from one another at 99.999% the speed of light. It would be a dark, cold, dead universe.
2- If It Was Thus, You Would Never Get To Ask This Question
This should be self-evident.