Dear m.michna

Normally it is better that you set a id for the td tag of your search textbox. The normal class for a textbox is in dnn: NormalTextbox.
For instance:

<td class="TdClassOfSearch" id="Srch"><dnn:SEARCH runat="server" id="dnnSEARCH" Submit="Search&nbsp;&raquo;" CssClass="SrchLink" /></td>

And the you can set the different classes that you need
for instance:

#Srch .NormalTextbox {
   width: 120px;
}
.TdClassOfSearch {}
.SrchLink:link, .SrchLink:visited {}
.SrchLink:hover {}
.SrchLink:active, .SrchLink:focus {}
.SrchLink:active:hover {}