This week the weather forecast currently does not look too bad but conditions change quickly in the Sierras in winter. In the mountains in winter you should be prepared for the unpredictability by carrying chains. I've seen the rangers both check and not check but better to be prepared.
As said chains are easy to rent, some of the Fresno area gas stations even rent them. I have found that some rental prices are high enough to make simply buying chains an option.
It is not just a tire size purchase. Check your owners manual if using your own vehicle, some say no chains should be used while others say only use snow cables. We own one like that, it is a clearance problem behind the wheel.
If you are in a rental car check with the company since some contracts do not allow chains to be used on their vehicles.
The current forecast for Lodgepole is for a slight possibility of snow and rain (about 30%) on Wednesday night. Right now that doesn't look like it would cause a problem.
You can follow the forecast changes for Lodgepole here
As I posted on the other thread, conditions at Lodgepole will be different than Grant Grove. Lodgepole runs colder and snowier than Grant Grove.
If I remember correctly Wuksachi has a 48 hour cancellation policy. So you would want to check the forecast just before that time.
The one problem though would be that during/after snowfall the General's Highway can be closed temporarily for plowing. So even chains would not allow you to reach Wuksachi. I've gone to Grant Grove in winter and seen the General's Highway closed heading to Sequoia.
You can check on current road conditions in the park at (559) 565-3341, extension 941.
But as I said at least right now it looks like the weather will not be bad.