JSFiddle - React, Tailwind, and code Playground

HTML

<table border="0" cellpadding="0" cellspacing="0">
<tr><td><img src="http://blog.hanabi-fan.cz/wp-content/uploads/2014/11/zima.jpg" name="obdobi"></td></tr>
</table>

JavaScript

if (document.images) {
var myDate=new Date()
var day=myDate.getDate()
var month=myDate.getMonth()
var obdobi = 0 // zima    
    // Nejprve vypocet obdobi...
    if( (month>3) || ( (month==3) && (day>=1) ) )
        obdobi = 1;
    if( (month>6) || ( (month==6) && (day>=1) ) )
        obdobi = 2;
    if( (month>9) || ( (month==9) && (day>=1) ) )
        obdobi = 3;
    if( (month>12) || ( (month==12) && (day>=1) ) )
        obdobi = 0;
    // ...pote zmena obrazku dle vypocteneho obdobi
    switch( obdobi) {
        case 0: document.images.obdobi.src="http://blog.hanabi-fan.cz/wp-content/uploads/2014/11/zima.jpg";
            break;
        case 1: document.images.obdobi.src="http://blog.hanabi-fan.cz/wp-content/uploads/2014/07/jaro.jpg";
            break;
        case 2: document.images.obdobi.src="http://blog.hanabi-fan.cz/wp-content/uploads/2014/07/leto.jpg";
            break;
        case 3: document.images.obdobi.src="http://blog.hanabi-fan.cz/wp-content/uploads/2014/07/podzim.jpg";
            break;
    }
}