Write your code in $(document).ready block.
<script type="text/javascript" src="http://ajax.googleapis.com/ajax/libs/jquery/1.8.3/jquery.min.js"></script>
<script type="text/javascript">
    $(document).ready(function () {
        $("[id*=GridView1] td").bind("mouseout", function () {
            $(this).closest("tr").find("[id*=lnkDelete]").hide();
        });
    });
</script>
 Complete Sample:
HTML
<asp:GridView ID="GridView1" HeaderStyle-BackColor="#3AC0F2" HeaderStyle-ForeColor="White"
    runat="server" AutoGenerateColumns="false">
    <Columns>
        <asp:BoundField DataField="Id" HeaderText="Id" ItemStyle-Width="30" />
        <asp:BoundField DataField="Name" HeaderText="Name" ItemStyle-Width="150" />
        <asp:BoundField DataField="Country" HeaderText="Country" ItemStyle-Width="150" />
        <asp:TemplateField HeaderText="Delete">
            <ItemTemplate>
                <asp:Button ID="btnDelete" Text="Delete" runat="server" />
            </ItemTemplate>
        </asp:TemplateField>
    </Columns>
</asp:GridView>
jQuery
<script type="text/javascript">
    $(document).ready(function () {
        $("[id*=btnDelete]").hide();            
    });        
    $("[id*=GridView1] td").live("mouseout", function () {
        $(this).closest("tr").find("[id*=btnDelete]").hide();
    });
    $("[id*=GridView1] td").live("mouseover", function () {
        $(this).closest("tr").find("[id*=btnDelete]").show();
    });
</script>
Namespace
using System.Data;
C#
protected void Page_Load(object sender, EventArgs e)
{
    if (!this.IsPostBack)
    {
        DataTable dt = new DataTable();
        dt.Columns.AddRange(new DataColumn[3] { new DataColumn("Id", typeof(int)),
                        new DataColumn("Name", typeof(string)),
                        new DataColumn("Country",typeof(string)) });
        dt.Rows.Add(1, "John Hammond", "United States");
        dt.Rows.Add(2, "Mudassar Khan", "India");
        dt.Rows.Add(3, "Suzanne Mathews", "France");
        dt.Rows.Add(4, "Robert Schidner", "Russia");
        GridView1.DataSource = dt;
        GridView1.DataBind();
    }
}
Screenshot