Rain, mud and sometimes even snow are part of the game, and are not usually considered, "weather conditions are construed to be hazardous to life or limb of the participants". That's reserved for lightening and possibly volcanic action.
As for ball placement I would suggest focusing on the end zone pylons (if visible) or goal posts to help you judge where the ball might be placed across the width of the field, and using the wing official and some other permanent point to help establish where to spot the ball. It's not a good idea to keep the "ball boys" on the field, and although we usually don't like to see clean balls tossed into the field, working with the ball boy and wing official to lesson the chance of dropping it, tossing it it might be the best of available options.
Measurements are a tool to help the Referee determine reaching the Line to gain, requests from other parties are irrelevant and are simply rejected.
The Umpire holding the spot, and the ball, and placing it down when the snapper is on the line, may also be the best option available under certain conditions. The Umpire should have a towel with him, that may need to be changed often, but you have to do the best with what the circumstances allow.
As for a field being too sloppy to play (as opposed to potentially dangerous) that's a game management issue, although they might appreciate your advice. The single indispensible necessity for a football game is players, if one team decides not to play, there can be no game. Whatever will be the final disposition of a game, where either one or both teams decide not to play,because of "field conditions" other than thunder or lightening will be decided by game management and exceed our control.
Other than the rare situation of a forfeit, which is beyonf weather conditions, we do not terminate games. We may interrupt, cause a postponement or rescheduling, but the final decision about if, or when, to reschedule will be a game management issue.