Is it possible to refresh a timer in a Today Widget?

Yes you can. I have just tested and it works. You just have to add your timer to the main run loop NSRunLoopCommonModes:

RunLoop.main.add(yourTimerName, forMode: .commonModes)

---

import NotificationCenter

class TodayViewController: UIViewController, NCWidgetProviding {

    @IBOutlet weak var strTimer: UILabel!

    var timer = Timer()

    func updateInfo() {
        strTimer.text = Date().description
    }
    override func viewDidLoad() {
        super.viewDidLoad()
        timer = Timer.scheduledTimer(timeInterval: 1, target: self, selector: #selector(updateInfo), userInfo: nil, repeats: true)
        RunLoop.main.add(timer, forMode: .commonModes)
    }
    func widgetPerformUpdate(completionHandler: @escaping (NCUpdateResult) -> Void) {
        completionHandler(.newData)
    }
}

I know this is a Swift question, but I found it looking for Objective-C code and so others may too.

-(void) viewDidLoad
{
    [NSTimer scheduledTimerWithTimeInterval:1 // update more than once a second to appear in sync with the system clock
                                     target:self
                                   selector:@selector(updateUi:)
                                   userInfo:nil
                                    repeats:YES];

}


-(void) updateUi:(NSTimer *)timer 
{
   // Update Widget UI as required
}